Chapter 8: Q. 102 (page 772)

Use the Quotient Property to simplify square roots.
$\sqrt{\frac{150 r^{3}}{256}}$ .

Short Answer

Expert verified

The simplified form is $\frac{5 |r| \sqrt{6 r}}{16}$ .

Step by step solution

Step 1. Given information.

The radical expression as:

$\sqrt{\frac{150 r^{3}}{256}}$ .

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.

$\sqrt{\frac{150 r^{3}}{256}} = \sqrt{\frac{25 r^{2} . 6 r}{256}} = \frac{\sqrt{25 r^{2} . 6 r}}{\sqrt{256}} = \frac{\sqrt{{(5 r)}^{2}} \sqrt{6 r}}{16} = \frac{5 |r| \sqrt{6 r}}{16}$

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Use the Quotient Property to simplify square roots.
$\sqrt{\frac{150 r^{3}}{256}}$ .

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.150r3256.

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

Applied Mathematics

Discrete Mathematics

Geometry

Probability and Statistics

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

Use the Quotient Property to simplify square roots.
$\sqrt{\frac{150 r^{3}}{256}}$ .