Chapter 8: Q. 8.8TI (page 747)

Simplify: $(a) \sqrt[3]{- 216} (b) \sqrt[4]{- 81} (c) \sqrt[5]{1024}$

Short Answer

Expert verified

The solutions of (a) is $- 6$ , (b) is no real number and (c) is $- 4$

Step by step solution

Part (a). Step 1. Given information

The root: $\sqrt[3]{- 216}$

Part (a) Step 2. Calculation

We have,

$\sqrt[3]{- 216} = - 6$

Since, $- 6^{3} = - 216$

Therefore, the solution is $- 6$

Part (b). Step 1. Given information

The root: $\sqrt[4]{- 81}$

Part (b) Step 2. Calculation

We have,

$\sqrt[4]{- 81} N o t a r e a l n u m b e r$

No real number is raised to the fourth power is negative.

Part (c). Step 1. Given information

The root: $\sqrt[5]{- 1024}$

Part (c) Step 2. Calculation

We have,

$\sqrt[5]{- 1024} = - 4$

Since, ${(- 4)}^{5} = - 1024$

Therefore, the solution is $- 4$

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Simplify: $(a) \sqrt[3]{- 216} (b) \sqrt[4]{- 81} (c) \sqrt[5]{1024}$

Short Answer

Step by step solution

Part (a). Step 1. Given information

Part (a) Step 2. Calculation

Part (b). Step 1. Given information

Part (b) Step 2. Calculation

Part (c). Step 1. Given information

Part (c) Step 2. Calculation

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Simplify:(a)-2163(b)-814(c)10245

Short Answer

Step by step solution

Part (a). Step 1. Given information

Part (a) Step 2. Calculation

Part (b). Step 1. Given information

Part (b) Step 2. Calculation

Part (c). Step 1. Given information

Part (c) Step 2. Calculation

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Simplify: $(a) \sqrt[3]{- 216} (b) \sqrt[4]{- 81} (c) \sqrt[5]{1024}$