Copyright © Cengage Learning. All rights reserved. Functions 1 Basic Concepts

Copyright © Cengage Learning. All rights reserved. Unit 1C Review of Operations with Decimal Fractions and Percent

Copyright © Cengage Learning. All rights reserved. Powers and Roots 1.15

4 Powers and Roots The square of a number is the product of that number times itself. The square of 3 is 3  3 or 3 2 or 9. The square of a number may be found with a calculator as follows.

5 Example 1 Find rounded to three significant digits. Thus, = 5420 rounded to three significant digits.

6 Powers and Roots The square root of a number is that positive number which, when multiplied by itself, gives the original number. The square root of 25 is 5 and is written as. The symbol is called a radical.

7 Example 3 Find the square roots of a. 16, b. 64, c. 100, and d a. = 4 because 4  4 = 16 b. = 8 because 8  8 = 64 c. = 10 because 10  10 = 100 d. = 12 because 12  12 = 144 Numbers whose square roots are whole numbers are called perfect squares. For example,1, 4, 9, 16, 25, 36, 49, and 64 are perfect squares.

8 Powers and Roots The cube of a number is the product of that number times itself three times. The cube of 5 is 5  5  5 or 5 3 or 125.

9 Example 6 Find the cubes of a. 2, b. 3, c. 4, and d. 10. a. 2 3 = 2  2  2 b. 3 3 = 3  3  3 c. 4 3 = 4  4  4 d = 10  10  10 = 8 = 27 = 64 = 1000

10 Powers and Roots The cube root of a number is that number which, when multiplied by itself three times, gives the original number. The cube root of 8 is 2 and is written as. (Note: 2  2  2 = 8. The small 3 in the radical is called the index.)

11 Example 9 Find the cube roots of a. 8, b. 27, and c a. = 2 because 2  2  2 = 8 b. = 3 because 3  3  3 = 27 c. = 5 because 5  5  5 = 125

12 Powers and Roots Numbers whose cube roots are whole numbers are called perfect cubes. For example, 1, 8, 27, 64, 125, and 216 are perfect cubes. In general, in a power of a number, the exponent indicates the number of times the base is used as a factor. For example, the 4th power of 3 is written 3 4, which means that 3 is used as a factor 4 times (3 4 = 3  3  3  3 = 81).

13 Example 12 Find rounded to three significant digits. Thus, = 56.4 rounded to three significant digits.