4-7 Estimating Square Roots
California
Evaluating
Algebraic Expressions
Standards
NS2.4 Use the inverse relationship between
raising to a power and extracting the root of a
perfect square integer; for an integer that is not
a square, determine without a calculator the
two integers between which its square root
lies and explain why.
4-7 Estimating Square Roots
Additional Example 1: Estimating Square Roots of
Numbers
TheEvaluating
55 is between
two integers.
Name the
Algebraic
Expressions
integers. Explain your answer.
55
36, 49, 64, 81 List perfect squares near 55.
49 < 55 < 64
Find the perfect squares nearest 55.
49 < 55 < 64 Find the square roots of the perfect
squares.
7 < 55 < 8
55 is between 7 and 8 because 55 is between
49 and 64.
4-7 Estimating Square Roots
Check It Out! Example 1
The 80 is between two integers. Name the
Evaluating Algebraic Expressions
integers. Explain your answer.
80
49, 64, 81, 100 List perfect squares near 80.
64 < 80 < 81
Find the perfect squares nearest 80.
64 < 80 < 81 Find the square roots of the perfect
squares.
8 < 80 < 9
80 is between 8 and 9 because 80 is between
64 and 81.
4-7 Estimating Square Roots
Additional Example 2: Recreation Application
A Coast Guard boat searching for a lost sailboat
covers
a square area
of 185 mi2Expressions
. What is the
Evaluating
Algebraic
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 √185 .
144, 169, 196, 225
List perfect squares near 185.
169 < 185 < 196
Find the perfect squares nearest 185.
√169 < √185 < √196 Find the square roots of the perfect
squares.
13 < √185 < 14
185 is closer to 196 than to 169, so
√185  14
185 is closer to 14 than 13.
Each side of the search area is about 14 miles long.
4-7 Estimating Square Roots
Check It Out! Example 2
A tent was advertised in the newspaper as having
2. What is the
an enclosed
square
area
of
168
ft
Evaluating Algebraic Expressions
approximate length of the sides of the square
area? Round your answer to the nearest foot.
The length of each side of the square is √168
. near 168.
121, 144, 169, 196
List perfect squares
144 < 168 < 169
Find the perfect squares nearest 168.
√144 < √168 < √169 Find the square roots of the perfect
squares.
12 < √16 < 13
8
168 is closer to 169 than to 144, so
√168  13
168 is closer to 13 than 12.
Each side of the tent is about 13 feet long.