Chapter 9: Q 9.176 (page 1112)

Simplify: (a) $\sqrt[3]{1000}$ (b) $\sqrt[4]{16}$ (c) $\sqrt[5]{32}$

Short Answer

Expert verified

Part (a) $\sqrt[3]{1000} = 10$

Part (b) $\sqrt[4]{16} = 2$

Part (c) $\sqrt[5]{32} = 2$

Step by step solution

Part (a) Step 1: Given information

The given expression is $\sqrt[3]{1000}$ . $\sqrt[3]{1000}$

Part (a) Step 2: Simplification

Using the formula of ${(a^{m})}^{\frac{1}{m}} = a^{m \times \frac{1}{m}}$

$\sqrt[3]{1000} = {(1000)}^{\frac{1}{3}} = {(10^{3})}^{\frac{1}{3}} = 10^{3 \times \frac{1}{3}} = 10$

Hence, $\sqrt[3]{1000} = 10$

Part (b) Step 1: Given information

The given expression is $\sqrt[4]{16}$ .

Part (b) Step 2: Simplification

Using the formula of ${(a^{m})}^{\frac{1}{n}} = a^{m \times \frac{1}{n}}$

$\sqrt[4]{16} = {(16)}^{\frac{1}{4}} = {(2^{4})}^{\frac{1}{4}} = 2^{4 \times \frac{1}{4}} = 2$

Hence, $\sqrt[4]{16} = 2$

Part (c ) Step 1: Given information

The given expression is $\sqrt[5]{32}$ .

Part (c) Step 2: Simplification

Using the formula of ${(a^{m})}^{\frac{1}{m}} = a^{m \times \frac{1}{m}}$

role="math" localid="1648808974316" $\sqrt[5]{32} = {(32)}^{\frac{1}{5}} = {(2^{5})}^{\frac{1}{5}} = 2$

Hence, $\sqrt[5]{32}$ is $2$

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Simplify: (a) $\sqrt[3]{1000}$ (b) $\sqrt[4]{16}$ (c) $\sqrt[5]{32}$

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Simplification

Part (b) Step 1: Given information

Part (b) Step 2: Simplification

Part (c ) Step 1: Given information

Part (c) Step 2: Simplification

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Simplify: (a)10003(b) 164(c)325

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Simplification

Part (b) Step 1: Given information

Part (b) Step 2: Simplification

Part (c ) Step 1: Given information

Part (c) Step 2: Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Simplify: (a) $\sqrt[3]{1000}$ (b) $\sqrt[4]{16}$ (c) $\sqrt[5]{32}$