Jan 28, 2024 · Sqrt 1+sint = sqrt.(sint/2 +cost/2)^2 Which gives .(sint/2 +cost/2). As square root and square cancel out. And Laplace of (sint/2 +cost/2) will give you the answer. Share. Cite. Follow answered May 17, 2017 at 17:14. Hailmogambo Hailmogambo. 1 $\endgroup$ 1. 2 $\begingroup$ You must learn basic MATHJAX. See ...taylor series of sqrt (1-x) - Wolfram|Alpha. taylor series of sqrt (1-x) Natural Language. Math Input. Extended Keyboard. Examples. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics ...Algebra. Simplify square root of 98. √98 98. Rewrite 98 98 as 72 ⋅2 7 2 ⋅ 2. Tap for more steps... √72 ⋅2 7 2 ⋅ 2. Pull terms out from under the radical. 7√2 7 2. The result can be shown in multiple forms. -1 is 1 rotated over $\pi$ radians. The square root of a number on the unit circle is the number rotated over half the angle, so $i$, or $\sqrt{-1}$ is 1 rotated over $\pi/2$ …The square root of a negative number is not a real number but a complex number. It is because the square of any integer is a positive value. The square root of a negative number, say, -y, is: √(-y)= i√y, where ‘i’ is the square root of -1. Square root of Complex Numbers. To find the square root of complex numbers is a little complicated. sqrt(3) Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math ...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeStack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeYes, square roots can create 2 answers -- the positive (principal) root and the negative root. When you are working with square roots in an expression, you need to know which value you are expected to use. The default is the principal root. We only use the negative root when there is a minus in front of the radical. For example: 8 + sqrt (9) = 11. Power series with a positive convergence radius give holomorphic functions. If a power series (centered at the origin) converges to $\sqrt{1-x}$ over a neighbourhood of the origin, it has to be the Maclaurin series of $\sqrt{1-x}$, namely $$ \sum_{n\geq 0}\frac{\binom{2n}{n}}{4^n(1-2n)}x^n $$ by the principle of analytic continuation.a, b < 0. If a and b are negative, then the square root of them must be imaginary: ⁺√a = xi. ⁺√b = yi. x and y must be positive (and of course real), because we are dealing with the principal square roots. ⁺√a • ⁺√b = xi (yi) = -xy. -xy must be a negative real number because x and y are both positive real numbers. integral of 1/ (x sqrt (1+x+x^2)) Natural Language. Math Input. Extended Keyboard. Examples. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music….Did you know that the solution of the equation 1 + sqrt(3x + 3) = sqrt(7x + 2) can be found through algebraic manipulation? By isolating the radical terms on one side and squaring both sides of the equation, you can simplify the expression and solve for the value of x.Method 1: That makes, ... What is −9 × −9? https://www.quora.com/What-is-sqrt-9-times-sqrt-9 TL;DR You can never take a negative square root, and the answer can never be …We couldn't describe $\sqrt{-1}$ with a real number, since the square of a positive number is positive, and the square of a negative number is positive. There is no real number whose square is negative. The square root of a real number is not always a real number. It turns out that $\sqrt{-1}$ is a rather curious number, which you can read ... sqrt(-1) Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on …Apr 14, 2011 ... 3 Answers 3 · The square root of 1 is 1. · This is because the number 1 has the special property 1⋅1=1. This is not true for 2, for instance: 2 ...Mar 23, 2018 ... Why is sqrt(-1) treated as mathematically permissible to work with if replaced with the imaginary unit, whereas dividing by zero is just never ...Dec 17, 2018 ... reduce sqrt(1/81), the square root of 1/81.HINT: y2k = 0, y2k+1 = k+1/(2k+1). sqrt (10) No simplification exists, Root remains : • sqrt (10) Simplify : sqrt (10) Factor 10 into its prime factors 10 = 2 • 5 To simplify a square root, we extract factors ... sqrt (11) No simplification exists, Root remains : • sqrt (11) Simplify : sqrt (11) Factor 11 into its prime factors 11 = 11 ... The principal square root is always the positive root. For example, the principal root of sqrt(9) = 3. But, sqrt(9) has 2 roots. If both roots are needed, usually when solving quadratic …How do you find the value of #tan^-1 sqrt(3)#? Trigonometry Inverse Trigonometric Functions Basic Inverse Trigonometric Functions. 1 AnswerTo calculate the square root of a negative number, find the square root of the same positive number and multiply by "i". ( where i represents an imaginary number and i = square root of -1) Example: square root of -5. = (square root of 5) x (square root of -1) = (square root of 5) x (i) = 2.236068 x i. = 2.236068i. Jun 1, 2018 ... See a solution process below: Square root of 1/2 = sqrt(1/2) We can use this rule for radicals to rewrite the expression: ...1/sqrt (x), sqrt (x), sqrt (x)^2. continued fraction theorems that hold for sqrt (6) tangent at sqrt (x) at x = 6. regular continued fraction expansion of square roots of rational numbers. Have a question about using Wolfram|Alpha? Contact Pro Premium Expert Support ». Give us your feedback ». Compute answers using Wolfram's breakthrough ...WolframAlpha Online Integral Calculator Solve integrals with Wolfram|Alpha x sin x2 d x Natural Language Math Input More than just an online integral solver Wolfram|Alpha is a …Jan 30, 2015 ... Integral of 1/sqrt(1-x^2) from 0 to sqrt(3)/2, Please subscribe and share my videos to help my channel grow! Comment #bprpYAY down below ...integrate x/(x-1) integrate x sin(x^2) integrate x sqrt(1-sqrt(x)) integrate x/(x+1)^3 from 0 to infinity; integrate 1/(cos(x)+2) from 0 to 2pi; integrate x^2 sin y dx dy, x=0 to 1, y=0 to pi; View more examples; Access instant learning tools. Get immediate feedback and guidance with step-by-step solutions for integrals and Wolfram Problem ... Method 1: That makes, ... What is −9 × −9? https://www.quora.com/What-is-sqrt-9-times-sqrt-9 TL;DR You can never take a negative square root, and the answer can never be …From Wikipedia, the free encyclopedia "Square roots" redirects here. For other uses, see Square Roots (disambiguation). Notation for the (principal) square root of x. For example, …The procedure to use the square root calculator is as follows: Step 1: Enter the number in the respective input field. Step 2: Now click the button “Find Square Root” to get the output. Step 3: The square root of the given number will be displayed in the output field. 🏼 https://integralsforyou.com - Integral of sqrt(1-cos(x)) - How to integrate it step by step using integration by substitution!🙈 𝐒𝐚𝐦𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚?...sum sqrt (n) from n = 1 to n. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music….Nov 14, 2019 ... Integral of sqrt(1+tan(x)), harder than the integral of sqrt(tan(x)), see my 100 integrals video https://youtu.be/dgm4-3-Iv3s If you enjoy ...Here's another way to do it, without using reduction formulas or hyperbolic functions. Let: #x = tantheta# #dx = sec^2thetad theta# #=> int sqrt(tan^2theta + 1)sec^2thetad theta#15 ÷ 1.388 7 = 1.403. (1.403 × 7 + 1.388)/8 = 1.402. It should then be clear that computing any further will result in a number that would round to 1.403, making 1.403 the final estimate to 3 decimal places. This free root calculator determines the roots of numbers, including common roots such as a square root or a cubed root. integral of 1/ (x sqrt (1+x+x^2)) Natural Language. Math Input. Extended Keyboard. Examples. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music….Jan 26, 2017 ... How To prove that 3=sqrt(1+2sqrt(1+3sqrt(1+4sqrt(1+...)))) Website: https://www.mathematicsart.com Like Art Of Mathematics on Facebook ...Apr 14, 2011 ... 3 Answers 3 · The square root of 1 is 1. · This is because the number 1 has the special property 1⋅1=1. This is not true for 2, for instance: 2 ...Algebra. Simplify - square root of 1/25. −√ 1 25 - 1 25. Rewrite √ 1 25 1 25 as √1 √25 1 25. − √1 √25 - 1 25. Any root of 1 1 is 1 1. − 1 √25 - 1 25. Simplify the denominator. Tap for more steps... Feb 17, 2015 ... here's how to integrate x/sqrt(1-x^2) https://www.youtube.com/watch?v=B1hm9iSzu_E Integral of sqrt((1-x)/(1+x)) Subscribe to ...sqrt (27a) Simplified Root : 3 • sqrt (3a) Simplify : sqrt (27a) Step 1 :Simplify the Integer part of the SQRT Factor 27 into its prime factors 27 = 33 To simplify a square ... sqrt (377) No simplification exists, Root remains : • sqrt (377) Simplify : sqrt (377) Factor 377 into its prime factors 377 = 13 • 29 To simplify a square root ...The correct Answer is:C ... Step by step video, text & image solution for sqrt(1+sqrt(1+sqrt(1+…..))) by Maths experts to help you in doubts & scoring excellent ...Mar 29, 2018 · The answer is =1/2arcsinx+1/2xsqrt (1-x^2)+C Let x=sintheta, =>, dx=costhetad theta costheta=sqrt (1-x^2) sin2theta=2sinthetacostheta=2xsqrt (1-x^2) Therefore, the integral is I=intsqrt (1-x^2)dx=intcostheta*costheta d theta =intcos^2thetad theta cos2theta=2cos^2theta-1 cos^2theta= (1+cos2theta)/2 Therefore, I=1/2int (1+cos2theta)d theta =1/2 ... For example, the square root of 1 is 1, because 1 x 1 = 1. This means the square root of 1 is 1. How do you calculate the square root of 1 in Excel or Google Sheets? To automatically calculate the square root of 1 in Excel or Google Sheets you need to use the SQRT() function: SQRT(1) Placing the above into a cell will automatically display the ... Nov 20, 2016 ... https://integralsforyou.com - Integral of 1/sqrt(1+x^2) - How to integrate it step by step using integration by substitution!Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...Free Square Root calculator - Find square roots of any number step-by-stepTo develop a better approximation of a square root, consider which perfect square the number is closer to. Approximate \ (\sqrt {6}\) to one decimal place. Below is a graph of …Aug 17, 2023 · Use this calculator to find the principal square root and roots of positive and negative real numbers. It will also tell you if the number is a perfect square or not, and the complex or imaginary solutions for negative numbers. Integral of 1/sqrt(e^x - 1) - How to integrate it step by step using the substitution method!👋 Follow @integralsforyou on Instagram for a daily integral 😉?...3 days ago · The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5. It is more precisely called the principal square root of 5, to distinguish it from the negative number with the same property. This number appears in the fractional expression for the golden ratio. It can be denoted in surd form as: It is ...Oct 1, 2023 ... limit of 1/(t*sqrt(1+t)) - 1/t when t goes to 0 | calculus 1 limit | L'Hôpital's rule.Feb 15, 2015 ... Integral of sqrt(1-4x^2), Trig Substitution, Stewart Calc 7th ET ed Trig Substitution, calculus 2 tutorial. Check out my 100 integrals: ...I've found an interesting floating point problem. I have to calculate several square roots in my code, and the expression is like this: sqrt(1.0 - pow(pos,2)) where pos goes from -1.0 to 1.0 in a...5 Answers. The binomial formula shows you that (1 + √2)n = an + bn√2 for some integers an, bn. But, the same binomial formula shows you that (convince yourself of this) (1 − √2)n = an − bn√2 for the same. − 1 2 2(1 − √2)n Now conclude that a2n = 2b2n + 1, so that (1 + 2)n = n + b √2 = √ 2n + √a2n − 1.Algebra. Simplify square root of 28. √28 28. Rewrite 28 28 as 22 ⋅7 2 2 ⋅ 7. Tap for more steps... √22 ⋅7 2 2 ⋅ 7. Pull terms out from under the radical. 2√7 2 7. The result can be shown in multiple forms. The square root of 1 is 1, since 1 × 1 = 1. Learn more about the square root symbol, definition, formula, and properties with examples and graphs.The square root of 1 is 1, since 1 × 1 = 1. Learn more about the square root symbol, definition, formula, and properties with examples and graphs. Integration. ∫ 01 xe−x2dx. Limits. x→−3lim x2 + 2x − 3x2 − 9. Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.Square Root Calculator. Every nonnegative real number a has a unique nonnegative square root, called the principal square root, which is denoted by √ a, where √ is called the radical sign or radix. For example, the principal square root of 9 is 3, denoted √ 9 = 3. √. = ? Calculator to give out the square root result of a positive number. 3 years ago. Yes, you can take that approach. But, your work is incomplete. When you simplify a square root, you need to ensure you have removed all perfect squares. With 3√8, you still have a perfect square inside the radical. 3√8 = 3√ (4*2) = 3√4 * √2 = 3*2√2 = 6√2. Hope this helps. Sometimes It helps to know some Pythagorean identities: If we solve for the first one, we can see that sin^2x=1-cos^2x. Substitute this inside the square root. Note that x is just a dummy variable, we could use theta instead: sqrt(sin^2theta)=-sintheta Simplify the left side: +-sintheta=-sintheta Since sintheta is an odd function, we can only conclude …Giải các bài toán của bạn sử dụng công cụ giải toán miễn phí của chúng tôi với lời giải theo từng bước. Công cụ giải toán của chúng tôi hỗ trợ bài toán cơ ...Subtract consecutive odd numbers (1, 3, 5, 7, etc.) starting with 1, from the number whose square root you are trying to find until you arrive at 0. For example: 9 - 1 = 8; 8 - 3 = 5; 5 - 5 = 0; You performed 3 subtractions to 0. The square root of 9 is 3. Prime Factorization. There are four steps involved in this method. Did you know that the solution of the equation 1 + sqrt(3x + 3) = sqrt(7x + 2) can be found through algebraic manipulation? By isolating the radical terms on one side and squaring both sides of the equation, you can simplify the expression and solve for the value of x.plot 1/sqrt(x) Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science ...taylor series of sqrt(1+x) Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For …Solve an equation, inequality or a system. Example: 2x-1=y,2y+3=x. 1: 2: 3: 4: 5: 6: 7: 8: 9: 0., < > ≤: ≥ ^ √: ⬅: : F _ ÷ | (* / ⌫ A: ↻: x: y = +-G ...3 days ago · 1.73205 08075 68877 2935... The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is denoted mathematically as or . It is more precisely called the principal square root of 3 to distinguish it from the negative number with the same property. The square root of 3 is an irrational number.Aug 17, 2023 · Calculator Use. Use this calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x is positive a will be positive. If x is negative a will be negative. The Cube Root Calculator is a specialized form of our common Radicals Calculator.Solve an equation, inequality or a system. Example: 2x-1=y,2y+3=x. 1: 2: 3: 4: 5: 6: 7: 8: 9: 0., < > ≤: ≥ ^ √: ⬅: : F _ ÷ | (* / ⌫ A: ↻: x: y = +-G ...Algebra. Simplify 1/ ( square root of 3) 1 √3 1 3. Multiply 1 √3 1 3 by √3 √3 3 3. 1 √3 ⋅ √3 √3 1 3 ⋅ 3 3. Combine and simplify the denominator. Tap for more steps... √3 3 3 3. The result can be shown in multiple forms. sqrt(-1) Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by ... 1/sqrt (2) in base 16. Have a question about using Wolfram|Alpha? Contact Pro Premium Expert Support ». Give us your feedback ». Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics ...Jan 29, 2012 · 3. Why is the result of sqrt(-1)*sqrt(-1) equal to -1 and not 1? This is because when multiplying two imaginary numbers, their values are multiplied but their exponents are added. In this case, sqrt(-1) has an exponent of 1/2, so when multiplied by itself, the exponent becomes 1. Therefore, the result is -1 instead of 1. 4.Jul 20, 2013 ... 7 Answers 7 ... The latest addendum to the Numpy Documentation here, adds the command numpy.emath.sqrt which returns the complex numbers when the ...Determine the Square Root: Since 1 × 1 = 1, the square root of 1 is 1. The square root of a number is defined as the value that, when multiplied by itself, gives the original number. Representing the Square Root of 1 Mathematically: As a Simple Number: The square root of 1 is exactly 1, so it is written as √1 = 1. Using the Radical Symbol: The square root of a number has the exponent of 1/2. The square root formula is used to find the square root of a number. We know the exponent formula: \(\sqrt[\text{n}]{x}\) = x 1/n. When n = 2, we call it square root. We can use any of the above methods for finding the square root, such as prime factorization, and so on. 9 1/2 = √9 = √(3 ... May 2, 2023 ... Our Website: https://linktr.ee/mathstoon In this video, we will find the square root of 1/36 in a very easy way. Subscribe for more videos ...There is a fun method for calculating a square root that gets more and more accurate each time around: a) start with a guess (let's guess 4 is the square root of 10) b) divide by the guess (10/4 = 2.5) c) add that to the guess (4 + 2.5 = 6.5) d) then divide that result by 2, in other words halve it. (6.5/2 = 3.25) So the question is how to simplify $\sqrt{1+\sqrt 2}$, or is it in the most simplified form? Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, ...Square root is common function in mathematics. It has a wide range of applications from the field of mathematics to physics. Sometimes it gets hard to calculate square root of a number, especially the one which are not actually square of a number. Often the method we employ are to tedious work with decimals. Here is a guide to find square root or rather their …🏼 https://integralsforyou.com - Integral of 1/sqrt(1+x^2) - How to integrate it step by step using integration by substitution! 𝐃𝐞𝐫𝐢𝐯𝐚𝐭𝐞 𝐭𝐨 𝐜𝐡...Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-stepHere's another way to do it, without using reduction formulas or hyperbolic functions. Let: #x = tantheta# #dx = sec^2thetad theta# #=> int sqrt(tan^2theta + 1)sec^2thetad theta#Learn what is the square root of 1, how to find it using different methods, and its applications in geometry and algebra. The square root of 1 is 1, a rational number and a perfect square. Can anyone show how to calculate $$\int\sqrt{1+u^2}\,du?$$ I can't calculate it. Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, ...Algebra. Simplify square root of 108. √108 108. Rewrite 108 108 as 62 ⋅3 6 2 ⋅ 3. Tap for more steps... √62 ⋅3 6 2 ⋅ 3. Pull terms out from under the radical. 6√3 6 3. The result can be shown in multiple forms.
Nov 21, 2023 · The square root of a number is a number multiplied times itself. The {eq}\sqrt-1 = \pm i {/eq}. The unit i was developed years ago when trying to find a solution to the equation {eq}x^2 + 1 = 0 {/eq}. . John lennon songs
Algebra. Simplify square root of 1/16. √ 1 16 1 16. Rewrite √ 1 16 1 16 as √1 √16 1 16. √1 √16 1 16. Any root of 1 1 is 1 1. 1 √16 1 16. Simplify the denominator. Tap for more steps... sqrt(3) Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math ...Aug 17, 2023 · Calculator Use. Use this calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x is positive a will be positive. If x is negative a will be negative. The Cube Root Calculator is a specialized form of our common Radicals Calculator.Yes, square roots can create 2 answers -- the positive (principal) root and the negative root. When you are working with square roots in an expression, you need to know which value you are expected to use. The default is the principal root. We only use the negative root when there is a minus in front of the radical. For example: 8 + sqrt (9) = 11. find the volume of the y= (sqrt (x)) (x-1) revolved around y axis, 0<=x<=1. Natural Language. Math Input. Extended Keyboard. Examples. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, …d^n/dx^n f [x^2] polar plot abs (1/sqrt (theta)) limit of (1/sqrt (eps + x)/1/sqrt (x))^ (1/eps) as eps -> 0. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music….So the question is how to simplify $\sqrt{1+\sqrt 2}$, or is it in the most simplified form? Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, ...3 days ago · The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5. It is more precisely called the principal square root of 5, to distinguish it from the negative number with the same property. This number appears in the fractional expression for the golden ratio. It can be denoted in surd form as: It is ...Algebra. Simplify 1/ ( square root of 3) 1 √3 1 3. Multiply 1 √3 1 3 by √3 √3 3 3. 1 √3 ⋅ √3 √3 1 3 ⋅ 3 3. Combine and simplify the denominator. Tap for more steps... √3 3 3 3. The result can be shown in multiple forms. Algebra. Evaluate square root of 1/4. √ 1 4 1 4. Rewrite √1 4 1 4 as √1 √4 1 4. √1 √4 1 4. Any root of 1 1 is 1 1. 1 √4 1 4. Simplify the denominator.The square root of 1 is +1 . It is just because square root is a non-negative mathematical operator which means that the number or expression to the RHS of square root can't be negative. So if. √ (a) = b , where 'a' and 'b' are real numbers and 'a' is a non-negative number, then. 'b' must be non-negative.Sep 20, 2015 · The principal square root of minus one is i. It has another square root -i. I really dislike the expression "the square root of minus one". Like all non-zero numbers, -1 has two square roots, which we call i and -i. If x is a Real number then x^2 >= 0, so we need to look beyond the Real numbers to find a square root of -1. Complex numbers can be thought of as an extension of Real numbers from ... Algebra. Simplify 1/ ( square root of 3) 1 √3 1 3. Multiply 1 √3 1 3 by √3 √3 3 3. 1 √3 ⋅ √3 √3 1 3 ⋅ 3 3. Combine and simplify the denominator. Tap for more steps... √3 3 3 3. The result can be shown in multiple forms. This isn't premature optimization, but rather avoiding premature pessimization (ref. no. 28, C++ coding standards, A.Alexandrescu). If math.sqrt is a more optimized routine (as it is) and expresses the intent more clearly, it should always be preferred over x**.5.It is not premature optimization to know what you write, and chose the alternative that is faster …Step 4.6.1. Use to rewrite as . Step 4.6.2. Apply the power rule and multiply exponents, . Step 4.6.3. Combine and . Step 4.6.4. Cancel the common factor of . Tap for more steps... Step 4.6.4.1. Cancel the common factor. Step 4.6.4.2. Rewrite the expression. Step 4.6.5. Evaluate the exponent. Step 5. The result can be shown in ....