Chapter 11: Q. 96 (page 1069)

In the following exercises, use the Quotient Property to simplify square roots.
$\sqrt{\frac{108 y^{4}}{49}}$

Short Answer

Expert verified

The simplified expression is, $\frac{6 y^{2} \sqrt{3}}{7}$ .

Step by step solution

Step 1 Given expression is,

$\sqrt{\frac{108 y^{4}}{49}}$

The objective is, we need to simplify the given expression.

The quotient property is given by,

$\frac{a^{m}}{a^{n}} = a^{m - n}$

Also we know that, $\sqrt[n]{a^{n}} = |a|$ .

Step 2 Simplify the given expression.

$\sqrt{\frac{108 y^{4}}{49}} = \sqrt{\frac{36 y^{4} \cdot 3}{49}}$

Now use the quotient property.

$\sqrt{\frac{108 y^{4}}{49}} = \frac{\sqrt{36 y^{4} \cdot 3}}{\sqrt{49}} = \frac{\sqrt{{(6 y^{2})}^{2} \cdot \sqrt{3}}}{7} = \frac{6 y^{2} \cdot \sqrt{3}}{7}$

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In the following exercises, use the Quotient Property to simplify square roots.
$\sqrt{\frac{108 y^{4}}{49}}$

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 Simplify the given expression.

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In the following exercises, use the Quotient Property to simplify square roots.108y449

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 Simplify the given expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, use the Quotient Property to simplify square roots.
$\sqrt{\frac{108 y^{4}}{49}}$