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How to Find the Square Root of Imperfect Squares

After memorization of common math squares, perfect numbers become easier to identity, such as 64, 25 and 9. However, imperfect numbers present a significant challenge to mathematicians, because they result in irrational numbers. Imperfect square numbers are either negative square roots or imperfect numbers which the answer to the square root is not a whole number (a decimal). The best way to find the answer is with a scientific or modern calculator that also has a square root button, although you still may not be able to know the exact imperfect square root as many contain hundreds of numbers to infinity, such as the number pi.

Things You'll Need

  • Scientific calculator
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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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