9-7 Squares and Square Roots
IWBAT find and estimate square roots of
numbers.
9-7 Squares and Square Roots
Vocabulary
perfect square
square root
radical sign
9-7 Squares and Square Roots
A square with sides that
measure 3 units each has
an area of 3 · 3, or 32.
Notice that the area of
the square is represented
by a power in which the
base is the side length
and the exponent is 2. A
power in which the
exponent is 2 is called a
square.
Exponent
2
Base
9-7 Squares and Square Roots
EX 1A: Finding Squares of Numbers
Find each square.
122
Method 1: Use a model.
12
A = lw
12
A = 12 · 12
A = 144
The square of 12 is 144.
9-7 Squares and Square Roots
EX 1B: Finding Squares of Numbers
Find each square.
3.52
Method 2: Use a calculator.
Press 3.5
x2
ENTER
.
3.52 = 12.25
The square of 3.5 is 12.25.
9-7 Squares and Square Roots
WRITE:
A perfect square is the square of a whole
number. The number 36 is a perfect square
because 36 = 62 and 6 is a whole number.
The square root of a number is one of
the two equal factors of the number.
Four is a square root of 16 because
4 · 4 = 16. The symbol for a square
root is √
, which is called a radical
sign.
9-7 Squares and Square Roots
Reading Math
√16 = 4 is read as “The square root of 16
is 4.”
9-7 Squares and Square Roots
EX 2A: Finding Square Roots of Perfect Squares
Find each square root.
√16
Method 1: Use a model.
The square root of 16 is 4.
9-7 Squares and Square Roots
EX 2B: Finding Square Roots of Perfect Squares
Find each square root.
√676
Method 2: Use a calculator.
Press
2nd
x2 676
ENTER
.
√676 = 26
The square root of 676 is 26.
9-7 Squares and Square Roots
EX 3A: Estimating Square Roots
Estimate each square root to the nearest whole
number. Use a calculator to check your answer.
√40
36 < 40 < 49 Find the perfect squares nearest 40.
√36 < √40 < √49
6 < √40 < 7
√ 40  6
Find the square roots of 36 and 49.
40 is closer in value to 36 than to 49.
Check
√40  6.32455532033 Use a calculator to approximate √40.
6 is a reasonable estimate.
9-7 Squares and Square Roots
EX 3B: Estimating Square Roots
Estimate each square root to the nearest whole
number. Use a calculator to check your answer.
√79
64 < 79 < 81
Find the perfect squares nearest 79.
√64 < √79 < √81
8 < √79 < 9
√ 79  9
Find the square roots of 64 and 81.
79 is closer in value to 81 than to 64.
Check
√79  8.8881944
Use a calculator to approximate √79.
9 is a reasonable estimate.
9-7 Squares and Square Roots
EX 4: Recreation Application
A Coast Guard boat searching for a lost sailboat
covers a square area of 125 mi2. What is the
approximate length of each side of the square
area? Round your answer to the nearest mile.
The length of each side of the square is √125 .
121 < 125 < 144
Find the perfect squares nearest 125.
√121 < √125 < √144
11
< √125 < 12
√125  11
Find the square roots of 121 and 144.
125 is closer to 121 than to 144.
Each side of the search area is about 11 miles long.