Question

Use absolute value to evaluate. $\sqrt{\left(\frac{217}{311}\right)^{2}}$

Name: Problem 48, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2020-07-13T14:13:36-08:00
Duration: 35 s
Channel: Ankit Gupta
Description: Use absolute value to evaluate. √(((217)/(311))^2)

   Use absolute value to evaluate.
$\sqrt{\left(\frac{217}{311}\right)^{2}}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 48

Instant Answer

Solved by Expert Ankit Gupta

07/13/2020

Step 1

To square a fraction, we square the numerator and the denominator separately: $\left(\frac{217^2}{311^2}\right)$. Now, we have the expression inside the absolute value: $\sqrt{\frac{217^2}{311^2}}$. To take the square root of a fraction, we take the square root Show more…

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Use absolute value to evaluate. $\sqrt{\left(\frac{217}{311}\right)^{2}}$

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Key Concepts

Absolute Value

The absolute value function returns the non-negative value of a number, regardless of its sign. It is crucial in algebra when dealing with expressions like the square root of a square, ensuring that the outcome is always non-negative.

Square Root of a Square

Taking the square root of a squared quantity, as in ?(x²), results in the absolute value of x. This property is fundamental because it guarantees that the process of squaring and then taking the square root retrieves the non-negative magnitude of the original value.

Rational Numbers

Rational numbers are numbers that can be written as a fraction of two integers. Understanding how to manipulate these fractions—including operations like squaring and extracting square roots—is essential in many areas of algebra.

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