Chapter 6.1, Problem 21PE

For Exercise 21-38, evaluate the roots without using a calculator. Identify those that are not real numbers. (See Example 4.)

21. a. $\sqrt{64}$

b. $\sqrt[3]{64}$

c. $-\sqrt{64}$

d. $-\sqrt[3]{64}$

e. $\sqrt{-64}$

f. $\sqrt[3]{-64}$

Example 4

Identifying the nth Root of a Real Number

Simplify the expressions, if possible.

1. $\sqrt{4}$

$\sqrt[3]{64}$

$\sqrt[5]{-32}$

$\sqrt[4]{81}$

$\sqrt[6]{1,000,000}$

$\sqrt{-100}$

$\sqrt[4]{-16}$