Question

Use absolute value to evaluate. $\sqrt{\left(\frac{517}{711}\right)^{2}}$

Name: Problem 49, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2020-07-13T14:13:10-08:00
Duration: 31 s
Channel: Ankit Gupta
Description: Use absolute value to evaluate. √(((517)/(711))^2)

   Use absolute value to evaluate.
$\sqrt{\left(\frac{517}{711}\right)^{2}}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 49

Instant Answer

Solved by Expert Ankit Gupta

07/13/2020

Step 1

To evaluate this, we simply square the fraction: $\left(\frac{517}{711}\right)^{2} = \frac{517^2}{711^2} = \frac{267289}{505521}$. Now, we need to take the square root of this fraction: Show more…

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Use absolute value to evaluate. $\sqrt{\left(\frac{517}{711}\right)^{2}}$

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Key Concepts

Absolute Value

The absolute value of a number represents its distance from zero on the number line, always yielding a non-negative result regardless of the sign of the original number.

Square Root of a Square

Taking the square root of a number that has been squared results in its absolute value, as the operation is defined as sqrt(x²) = |x|. This property ensures that the result is non-negative.

Algebraic Simplification

Using properties such as sqrt(x²) = |x| is a common algebraic technique to simplify expressions, making it easier to handle operations on rational or complex numbers without ambiguity regarding their sign.

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