Chapter 8: Q. 67 (page 771)

In the following exercises, simplify using absolute value signs as needed.
$\sqrt{y^{11}} \sqrt[3]{r^{5}} \sqrt[4]{s^{10}}$

Short Answer

Expert verified

The expression in simplified form is $y^{5} \sqrt{y}, r \sqrt[3]{r^{2}}, s^{2} \sqrt[4]{s^{2}}$ respectively

Step by step solution

Given information

Given the expression $\sqrt{y^{11}}, \sqrt[3]{r^{5}}, \sqrt[4]{s^{10}}$

Using the product property and simplifying

Using the property, we get

$\sqrt{y^{11}} = \sqrt{y^{10} y} \sqrt{y^{11}} = \sqrt{y^{10}} \sqrt{y} \sqrt{y^{11}} = = y^{5} \sqrt{y}$

Simplify another expression

Simplifying, we get

$\sqrt[3]{r^{5}} = \sqrt[3]{r^{3} r^{2}} \sqrt[3]{r^{5}} = \sqrt[3]{r^{3}} \sqrt[3]{r^{2}} \sqrt[3]{r^{5}} = r \sqrt[3]{r^{2}}$

Simplifying another expression

Using the property, we get

$\sqrt[4]{s^{10}} = \sqrt[4]{s^{8} s^{2}} \sqrt[4]{s^{10}} = \sqrt[4]{s^{8}} \sqrt[4]{s^{2}} \sqrt[4]{s^{10}} = = s \sqrt[2]{s^{2}}$

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In the following exercises, simplify using absolute value signs as needed.
$\sqrt{y^{11}} \sqrt[3]{r^{5}} \sqrt[4]{s^{10}}$

Short Answer

Step by step solution

Given information

Using the product property and simplifying

Simplify another expression

Simplifying another expression

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In the following exercises, simplify using absolute value signs as needed.y11r53s104

Short Answer

Step by step solution

Given information

Using the product property and simplifying

Simplify another expression

Simplifying another expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Mechanics Maths

Calculus

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute value signs as needed.
$\sqrt{y^{11}} \sqrt[3]{r^{5}} \sqrt[4]{s^{10}}$