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

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 = 81. Area = 25. 9. 5. Area = 16. 4. 4. 5. 9.

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

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  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 = 81 Area = 25 9 5 Area = 16 4 4 5 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 Area = 20 2 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 = 425 – 16 9 • 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.) • 150 - 144 = 6 169 – 144 25 • 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: • 200 - 196 (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.) • 200 - 196 = 4225 - 196 29 • The square root of 200 is about 14 4/29.

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