Chapter 11: Q. 100 (page 1069)

Use the Quotient Property to simplify square roots.
$\sqrt{\frac{180 s^{10}}{144}}$

Short Answer

Expert verified

The simplified form is $\frac{6 |s^{5}| \sqrt{5}}{12}$ .

Step by step solution

Step 1. Given information.

The radical expression as:

$\sqrt{\frac{180 s^{10}}{144}}$ .

Step 2. Write the concept.

To determine a simplified form of a radical expression following formula is used:

$\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}} a n d \frac{\sqrt[n]{a}}{\sqrt[n]{b}} = \sqrt[n]{\frac{a}{b}}$

If $\sqrt[n]{a} a n d \sqrt[n]{b}$ are real numbers, $b \neq 0$ for any integer $n \geq 2$ .

Step 3. Calculation.

Simplifying the expression.

$\sqrt{\frac{180 s^{10}}{144}} = \sqrt{\frac{36 s^{10} \cdot 5}{144}} = \frac{\sqrt{36 s^{10} \cdot 5}}{\sqrt{144}} = \frac{{\sqrt{(6 s^{5}})}^{2} \cdot \sqrt{5}}{12} = \frac{6 {|s|}^{2} \sqrt{5}}{12}$

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Use the Quotient Property to simplify square roots.
$\sqrt{\frac{180 s^{10}}{144}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Calculation.

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Use the Quotient Property to simplify square roots.180s10144

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Logic and Functions

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

Use the Quotient Property to simplify square roots.
$\sqrt{\frac{180 s^{10}}{144}}$