Chapter 11: Q. 504 (page 1069)

In the following exercises, use the Quotient Property to simplify square roots.
$(a) \sqrt{\frac{28 p^{7}}{q^{2}}} (b) \sqrt[3]{\frac{81 s^{8}}{t^{3}}} (c) \sqrt[4]{\frac{64 p^{15}}{q^{12}}}$

Short Answer

Expert verified

The required answers are $\frac{2 p^{3} \sqrt{7 p}}{q}, \frac{3 s^{2} \sqrt[3]{3 s^{2}}}{t} a n d$ $\frac{2 p^{3} \sqrt[4]{4 p^{3}}}{q^{3}}$

Step by step solution

Step 1. Given Information

The given expressions are

$(a) \sqrt{\frac{28 p^{7}}{q^{2}}} (b) \sqrt[3]{\frac{81 s^{8}}{t^{3}}} (c) \sqrt[4]{\frac{64 p^{15}}{q^{12}}}$

Part(a) Step 1. Calculation

Simplify the expression by rewriting the fraction using quotient property and product property.
$\sqrt{\frac{28 p^{7}}{q^{2}}} = \frac{\sqrt{28 p^{7}}}{\sqrt{q^{2}}} = \frac{\sqrt{4 p^{6}} \times \sqrt{7 p}}{\sqrt{q^{2}}} = \frac{2 p^{3} \sqrt{7 p}}{q}$

Part(b) Step 1. Calculation

Simplify the expression by rewriting the fraction using quotient property and product property.
$\sqrt[3]{\frac{81 s^{8}}{t^{3}}} = \frac{\sqrt[3]{81 s^{8}}}{\sqrt[3]{t^{3}}} = \frac{\sqrt[3]{27 s^{6}} \times \sqrt[3]{3 s^{2}}}{\sqrt[3]{t^{3}}} = \frac{3 s^{2} \sqrt[3]{3 s^{2}}}{t}$

Part(c) Step 1. Calculation

Simplify the expression by rewriting the fraction using quotient property and product property.
$\sqrt[4]{\frac{64 p^{15}}{q^{12}}} = \frac{\sqrt[4]{64 p^{15}}}{\sqrt[4]{q^{12}}} = \frac{\sqrt[4]{16 p^{12}} \times \sqrt[4]{4 p^{3}}}{\sqrt[4]{q^{12}}} = \frac{2 p^{3} \sqrt[4]{4 p^{3}}}{q^{3}}$

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In the following exercises, use the Quotient Property to simplify square roots.
$(a) \sqrt{\frac{28 p^{7}}{q^{2}}} (b) \sqrt[3]{\frac{81 s^{8}}{t^{3}}} (c) \sqrt[4]{\frac{64 p^{15}}{q^{12}}}$

Short Answer

Step by step solution

Step 1. Given Information

Part(a) Step 1. Calculation

Part(b) Step 1. Calculation

Part(c) Step 1. Calculation

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In the following exercises, use the Quotient Property to simplify square roots.(a)28p7q2(b)81s8t33(c)64p15q124

Short Answer

Step by step solution

Step 1. Given Information

Part(a) Step 1. Calculation

Part(b) Step 1. Calculation

Part(c) Step 1. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Pure Maths

Decision Maths

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, use the Quotient Property to simplify square roots.
$(a) \sqrt{\frac{28 p^{7}}{q^{2}}} (b) \sqrt[3]{\frac{81 s^{8}}{t^{3}}} (c) \sqrt[4]{\frac{64 p^{15}}{q^{12}}}$