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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.6TI (page 747)

Simplify: $(a) \sqrt[3]{1000} (b) \sqrt[4]{16} (c) \sqrt[5]{243}$

Short Answer

Expert verified

The solution of (a), (b) and (c) are $10, 2 a n d 3$ respectively.

Step by step solution

01

Part (a). Step 1. Given information

The root: $\sqrt[3]{1000}$

02

Part (a) Step 2. Calculation

We have,

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

Since, $10^{3} = 1000$

Therefore, the solution is $10$

03

Part (b). Step 1. Given information

The root: $\sqrt[4]{16}$

04

Part (b) Step 2. Calculation

We have,

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

Since, ${(2)}^{4} = 16$

Therefore, the solution is $2$

05

Part (c). Step 1. Given information

The root: $\sqrt[5]{243}$

06

Part (c) Step 2. Calculation

We have,

$\sqrt[5]{243} = 3$

Since, ${(3)}^{5} = 243$

Therefore, the solution is $3$

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Most popular questions from this chapter

In the following exercises, simplify using absolute value signs as needed. $\sqrt{96 r^{3} s^{3}}, \sqrt[3]{80 x^{7} y^{6}}, \sqrt[4]{80 x^{8} y^{9}}$

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