Question

Use absolute value to evaluate. $\sqrt{\left(-\frac{271}{311}\right)^{2}}$

Name: Problem 47, 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. √((-(271)/(311))^2)

   Use absolute value to evaluate.
$\sqrt{\left(-\frac{271}{311}\right)^{2}}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 47

Instant Answer

Solved by Expert Ankit Gupta

07/13/2020

Step 1

First, we have the expression inside the parentheses: $-\frac{271}{311}$. Show more…

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Use absolute value to evaluate. $\sqrt{\left(-\frac{271}{311}\right)^{2}}$

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Key Concepts

Absolute Value

Absolute value represents the non-negative distance of a number from zero on the number line, disregarding its sign. It ensures that any negative input is converted to a positive output, which is crucial for understanding expressions that naturally require non-negative results.

Square Root

The square root function returns the non-negative number that, when multiplied by itself, yields the original value. This non-negativity (i.e., the principal square root) is key when simplifying expressions that involve squared terms.

Square Root of a Square

The property ?(x²) = |x| highlights the relationship between squaring and taking square roots. This means that when you square a number and then take the square root, you recover its absolute value, ensuring the result is always non-negative.

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