Question

Write as an absolute value. $\sqrt{\left(9 y^{4}-2 z^{3}\right)^{2}}$

Name: Problem 58, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2022-09-27T03:24:36-08:00
Duration: 58 s
Channel: Erika Bustos
Description: Write as an absolute value. √((9 y^4-2 z^3)^2)

   Write as an absolute value.
$\sqrt{\left(9 y^{4}-2 z^{3}\right)^{2}}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 58

Instant Answer

Solved by Expert Erika Bustos

09/27/2022

Step 1

Now, we take the square root of this expression: $\sqrt{(9y^4 - 2z^3)^2}$. Since the square root and the square are inverse operations, they cancel each other out, leaving us with the expression inside the square root: $9y^4 - 2z^3$. Show more…

Show all steps

Thanks for your feedback!

Write as an absolute value. $\sqrt{\left(9 y^{4}-2 z^{3}\right)^{2}}$

Play audio

Feedback

Erika Bustos and 93 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Absolute Value

The absolute value of a number or expression represents its distance from zero on the number line and is always nonnegative. In algebra, the absolute value function is used to denote the magnitude of a real number without regard to its sign.

Square Root of a Square

The property that the square root of a squared expression equals the absolute value of the original expression (i.e., ?(A²) = |A|) is fundamental in algebra. This is because squaring a real number removes any sign information, and the square root function always returns the nonnegative value.

Simplification of Radical Expressions

Simplifying radical expressions often involves recognizing when the expression inside a radical is a perfect square, which can be rewritten using the absolute value function. Mastery of this process is essential for reducing complex algebraic expressions to their simplest form.

Please give Ace some feedback