Chapter 8: Q. 8.49 (page 770)

Simplify:
$(a) \frac{\sqrt{98 z^{5}}}{\sqrt{2 z}} (b) \frac{\sqrt[3]{- 500}}{\sqrt[3]{2}} (c) \frac{\sqrt[4]{486 m^{11}}}{\sqrt[4]{3 m^{5}}} .$

Short Answer

Expert verified

Part a. After simplifying we get, $7 z^{2} .$

Part b. After simplifying we get, $- 5 \sqrt[3]{2} .$

Part c. After simplifying we get, $3 m \sqrt[4]{2 m^{2}} .$

Step by step solution

Part a Step 1. Use the Quotient property to write as one radical

Given: $\frac{\sqrt{98 z^{5}}}{\sqrt{2 z}}$

By using the property we can write as $\sqrt{\frac{98 z^{5}}{2 z}} .$

Part a Step 2: Simplify the fraction under the radical

By simplifying we get,

$\sqrt{\frac{98 z^{5}}{2 z}} = \sqrt{49 z^{5 - 1}} = \sqrt{{(7 z^{2})}^{2}} = 7 z^{2}$

Part b Step 1. Use the Quotient property to write as one radical

Given: $\frac{\sqrt[3]{- 500}}{\sqrt[3]{2}}$

By using the property we can write as $\sqrt[3]{\frac{- 500}{2}} .$

Part b Step 2: Simplify the fraction under the radical

By simplifying we get,

$\sqrt[3]{\frac{- 500}{2}} = \sqrt[3]{- 250} = \sqrt[3]{(- 5^{3}) \cdot 2} = - 5 \sqrt[3]{2}$

Part c Step 1. Use the Quotient property to write as one radical

Given: $\frac{\sqrt[4]{486 m^{11}}}{\sqrt[4]{3 m^{5}}}$

By using the property we can write as $\sqrt[4]{\frac{486 m^{11}}{3 m^{5}}} .$

Part c Step 2: Simplify the fraction under the radical

By simplifying we get,

$\sqrt[4]{\frac{486 m^{11}}{3 m^{5}}} = \sqrt[4]{162 m^{6}} = \sqrt[4]{{(3 m)}^{4}} \cdot \sqrt[4]{2 m^{2}} = 3 m \sqrt[4]{2 m^{2}}$

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Simplify:
$(a) \frac{\sqrt{98 z^{5}}}{\sqrt{2 z}} (b) \frac{\sqrt[3]{- 500}}{\sqrt[3]{2}} (c) \frac{\sqrt[4]{486 m^{11}}}{\sqrt[4]{3 m^{5}}} .$

Short Answer

Step by step solution

Part a Step 1. Use the Quotient property to write as one radical

Part a Step 2: Simplify the fraction under the radical

Part b Step 1. Use the Quotient property to write as one radical

Part b Step 2: Simplify the fraction under the radical

Part c Step 1. Use the Quotient property to write as one radical

Part c Step 2: Simplify the fraction under the radical

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Simplify:a98z52zb-500323c486m1143m54.

Short Answer

Step by step solution

Part a Step 1. Use the Quotient property to write as one radical

Part a Step 2: Simplify the fraction under the radical

Part b Step 1. Use the Quotient property to write as one radical

Part b Step 2: Simplify the fraction under the radical

Part c Step 1. Use the Quotient property to write as one radical

Part c Step 2: Simplify the fraction under the radical

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Geometry

Discrete Mathematics

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

Simplify:
$(a) \frac{\sqrt{98 z^{5}}}{\sqrt{2 z}} (b) \frac{\sqrt[3]{- 500}}{\sqrt[3]{2}} (c) \frac{\sqrt[4]{486 m^{11}}}{\sqrt[4]{3 m^{5}}} .$