 # How to Find the Square Root of a Non-Perfect Square

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

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

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

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.

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.

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.

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.

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