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Published byAaliyah Bordley Modified over 4 years ago

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

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**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

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**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

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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.

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**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.

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**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.

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**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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