Finding the square root of a non-perfect square can be done using approximations. One method, as demonstrated in the referenced video, involves expressing the non-perfect square as a difference from a nearby perfect square.
Here's a breakdown of the method:
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Identify a Nearby Perfect Square: Find a perfect square close to the number you want to find the square root of. For example, to find the square root of 32, the nearest perfect square is 36.
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Express as a Difference: Rewrite the original number as the perfect square minus a difference. In the example of finding √32, rewrite it as √(36 - 4).
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Calculate the Square Root of the Perfect Square: Find the square root of the perfect square part. In the example, √36 = 6.
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Approximate: Use the following approximation:
√(a - b) ≈ √a - (b / (2√a)) where a is the perfect square and b is the difference.
- In our example, this translates to: √32 ≈ √36 - (4 / (2√36)) = 6 - (4/(2*6)) = 6 - (4/12) = 6 - (1/3) = 6 - 0.333 = 5.667
Therefore, √32 is approximately 5.667. This is a quick approximation technique, and the accuracy depends on how close the perfect square is to the original number.
