How to Find the Square Root of Imperfect Squares

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Things You'll Need

Instructions

1

Evaluate a negative square as a perfect square, then keep the negative sign the same. Negative squares have a negative symbol or "-" in front of the square root sign. Start by figuring out the square root of the number under the symbol. For example, the square root of 64 is 8. Likewise, the negative square root of 64 is -8.
2

Estimate the imperfect square to the nearest integer when the answer is not a whole number. For example, find the square root of 33. This is an imperfect square because no whole number multiples itself to become 33. However, you find the closest square less than the imperfect square's answer by first calculating the square root of a perfect square near 33. For example, the square root of 25 is 5. Now find the square root of a number higher than 33 yet close, such as 36. The square root of 36 is 6. As 36 is closer to 33, the square root of 33 is closer to 6 but higher than 5.
3

Calculate imperfect squares on a calculator to find the exact number. Enter the number to find the imperfect square root, such as 5 or 11. Press the square root function button. Most likely, the imperfect square root is an irrational number, such as the square root of 3, which is 1.7320508075 and continued.
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