Question

Use absolute value to simplify. You may need to factor first. $\sqrt{x^{10}}$

Name: Problem 59, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2020-05-27T00:41:30-08:00
Duration: 24 s
Channel: Cory Kuzinski
Description: Use absolute value to simplify. You may need to factor first. √(x^10)

   Use absolute value to simplify. You may need to factor first.
$\sqrt{x^{10}}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 59

Instant Answer

Solved by Expert Cory Kuzinski

05/27/2020

Step 1

Now, we know that the absolute value of a number is always non-negative. So, we can rewrite $x^5$ as $|x|^5$ to ensure that the result is always non-negative. Show more…

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Use absolute value to simplify. You may need to factor first. $\sqrt{x^{10}}$

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Key Concepts

Absolute Value

The absolute value represents the non-negative magnitude of a number. When taking the square root of a squared expression, such as ?(x²), the result is the absolute value of x, written as |x|. This ensures that the result of the square root is non-negative.

Properties of Exponents

Exponent rules allow us to manipulate powers when simplifying expressions. Recognizing that an even power can be written as a square (for example, x^10 can be expressed as (x^5)²) is crucial. This transformation makes it easier to apply the square root operation to the expression.

Simplifying Radicals by Factoring

When simplifying radicals, especially those involving even powers, it is helpful to factor the expression into a perfect square. Once expressed as the square of another expression, the square root can be simplified directly by removing the square, while incorporating absolute value to account for any negative signs in the original variable.

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