Chapter 9: Q 446. (page 1124)

Simplify:
a) $\sqrt[3]{- 8}$
b) $\sqrt[4]{- 81}$
c) $\sqrt[5]{- 32}$

Short Answer

Expert verified

a) $\sqrt[3]{- 8} = - 2$

b) $\sqrt[4]{- 81} = N A$

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

Step by step solution

Part (a) Step 1: Given Information

The given expression is $\sqrt[3]{- 8}$ .

Part (a) Step 2: Simplification

As $- 8 = {(- 2)}^{3}$

Expression becomes $\sqrt[3]{{(- 2)}^{3}}$

Simplifying gives $- 2$

Part (b) Step 1: Given Information

The given expression is $\sqrt[4]{- 81}$

Part (b) Step 2: Simplification

Fourth power of any number cannot be equal to a negative number.

Hence, no real number exists.

Part (c) Step 1: Given Information

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

Part (c) Simplification

As ${(- 2)}^{5} = - 32$

Expression becomes $\sqrt[5]{{(- 2)}^{5}}$

Simplifying gives $- 2$

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Simplify:
a) $\sqrt[3]{- 8}$
b) $\sqrt[4]{- 81}$
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) Simplification

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Simplify:a) -83b) -814c)-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) Simplification

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

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Simplify:
a) $\sqrt[3]{- 8}$
b) $\sqrt[4]{- 81}$
c) $\sqrt[5]{- 32}$