1. How to Find the Square Root of a Non-Perfect Square

2. Perfect Squares 25, 16 and 81 are called perfect squares.
This means that if each of these numbers were the area of a square, the length of one side would be a whole number.
Area = 25
Area = 81 9 5
Area = 16 4 5 4 9

3. Perfect Squares 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 = 196
152 = 225
162 = 256
172 = 289
182 = 324
192 = 361
202 = 400

4. Non-Perfect Squares
What about the numbers in between all of the perfect squares?
Why isn’t 20 a perfect square?
20 can’t make a square with whole numbers. (Area)
Area = 20 1 20 4
Area = 20 2
Area = 20 5 10
The square root of 20 must be a decimal or fraction number between 4 and 5.

5. How to find an approximation of the square root of 20…
What two perfect squares does 20 lie between?
16 and 25
The square root of 16 is 4, so the square root of 20 must be a little more than 4.
How to find the “little more”
Set up a fraction.
The numerator is the difference between 20 and the perfect square less than 20. (20 – 16)
The denominator will be the difference between the perfect square greater than 20 and the perfect square less than 20. (25 – 16)
20 – 16 = 4 25 –
The square root of 20 is about 4 4/9.

6. How to find an approximation of the square root of 150…
150 lies between what two perfect squares?
144 & 169
The square root of 144 is 12. So the square root of 150 must be a little more than 12.
Set up the fraction:
150 – 144 (This is our number minus the perfect square below it.)
169 – 144 (This is the perfect square below our number minus the perfect square above our number.)
= –
The square root of 150 is about 12 6/25.

7. How to find an approximation of the square root of 200…
200 lies between what two perfect squares?
196 & 225
The square root of 196 is 14. So the square root of 200 must be a little more than 14.
Set up the fraction:
(This is our number minus the perfect square below it.)
225 – 196 (This is the perfect square below our number minus the perfect square above our number.) =
The square root of 200 is about 14 4/29.