Page 354 - Basic College Mathematics with Early Integers

4.6 SQUARE ROOTS AND THE PYTHAGOREAN THEOREM Objectives

Find the Square Root
of a Number.
Objective Finding Square Roots
Approximate Square Roots.
The square of a number is the number times itself. For example,
#
The square of 5 is 25 because 5 2 or 5 5 = 25. Use the Pythagorean Theorem.
The square of -5 is also 25 because 1-52 2 or 1-521-52 = 25.

Recall from Chapter 1 that the reverse process of squaring is finding a square
root. For example,
2
A square root of 25 is 5 because 5 = 25.
2
A square root of 25 is also -5 because 1-52 = 25.
Every positive number has two square roots. We see above that the square
roots of 25 are 5 and -5.
We use the symbol 1 , called a radical sign, to indicate the positive square
root of a nonnegative number. For example,
2
125 = 5 because 5 = 25 and 5 is positive.
2
19 = 3 because 3 = 9 and 3 is positive.

Square Root of a Number
The square root, 1 , of a positive number a is the positive number b whose
square is a. In symbols,
1a = b, if b = a
2
Also, 10 = 0.

Remember that the radical sign 1 is used to indicate the positive square root
of a nonnegative number.

Example 1 Find each square root. PRACTICE 1
Find each square root.
a. 249 b. 21 c. 281
a. 2100 b. 264
Solution: c. 2169 d. 20
2
a. 249 = 7 because 7 = 49
2
b. 21 = 1 because 1 = 1
2
c. 281 = 9 because 9 = 81
Work Practice 1
PRACTICE 2
1 1
Example 2 Find: Find:
A36 A4
1 1 1 1 1 Answers
Solution: = because # =
A36 6 6 6 36 1. a. 10 b. 8 c. 13 d. 0
1
Work Practice 2 2.
2
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