7th Grade
Chapter 10.2 Estimating Square Roots
While every number (N) has a square, not every number has a perfect Square Root.
PERFECT SQUARES are WHOLE Numbers:
12
1
22
4
32
9
42
16
52
25
62
36
72
49
82
64
92
81
102
100
112
121
122
144
132
169
142 Etc.
196
What is the Square Root of 22? √𝟐𝟐
Since 22 is between 16 and 25, the square root of 22 has to be between 4 and 5.
16 < 22 < 25 So
√𝟏𝟔 < √𝟐𝟐 < √𝟐𝟓
or
4 < ? < 5.
Since 22 is closer to 5 (3 away) compared to 16 (6 away), the Square Root will be closer to 5!
Estimate
√𝟖𝟓
So
√𝟖𝟏 < √𝟖𝟓 < √𝟏𝟎𝟎 or
9 < ? < 10.
After an accident, a police offer can estimate the speed (S) of a care before it skidded to a stop.
They use the formula:
𝑠=
√𝟑𝟎 ∗ 𝒅 ∗ 𝒇
where
s is the speed in Miles Per Hour, d is the length of
the skid marks in feet and f is a value that depends on weather conditions. (Historic data collection).
What is the APPROXIMATE speed of a car that produced skid marks 90’ long with a f value of 1.2?
𝑠 ≈ √𝟑𝟎 ∗ 𝒅 ∗ 𝒇
or
𝑠 ≈ √𝟑𝟎 ∗ 𝟗𝟎 ∗ 𝟏. 𝟐
𝑺 ≈ 𝟓𝟔. 𝟗
≈ √𝟑, 𝟐𝟒𝟎