Lesson 12
Square Roots
 Taking
the square root of a number is
the opposite of squaring the number.
 You square a number when you multiply
a number by itself.
 To square 14, multiply 14 x 14 = 196, or
142 = 196.
 You can say 14 squared is 196.
 Square
numbers get their name from
the square figure.
3
3
 The area of this
32, or 3 squared
square is 3 x 3, or
.
 The
opposite, or inverse, of
squaring a number is taking the
square root
 The square root of 196 is 14, since
142 is 196.
 The square root of 100 is 10, since
102 is 100.
 The symbol for square root is 
 You write 196 = 14 and 100 =
10.
Example 1
 Find
the square root of 289 without a
calculator.
 Strategy: 289 is between 100
and 400.
 Step 1: What is 100? 100 = 10
 Step 2: What is 400? 400 = 20,
since 202 =400
3: Try 152; 152 = 225, so
289 is between 15 and 20.
 Step 4: Try 16 and 17
162 = 256 too small, 172 = 289 correct
 Step
Solution
 Since
172 = 289, 289 = 17.
Example 2
 Use
you calculator to find 85 to the
nearest hundredths place.
 Strategy: Understand how to use the
square root key on your calculator.
 Step 1: Key in the problem.
85 = 9.2195444
Solution
 85
= 9.22
Example 3
=
 Strategy: Remember, taking the square
root means finding a number whose
square is the number under the square
root sign.
 ¼
 Step
1: Find the square root of the
numerator. 1 = 1
 Step 2: Find the square root of the
denominator. 4 = 2
Solution
 The
¼ = ½, since ½ x ½ = ¼.