Q:

# What is the square root of 20?

A:

The square root of 20 is either 4.47, rounded to the nearest hundredth, or 2 times the square root of 5. The decimal answer is 4.47, and 2 times the square root of 5 is a more precise answer.

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To square a number is to multiply that number by itself. Perfect squares like 25 and 100 are the result of a whole number being multiplied by itself. Most numbers are not the result of a number being multiplied by itself, so taking their square roots does not result in a perfect whole number.

One can avoid answering in decimals by breaking a number down into multiplicative factors, one of which is perfect squares. For 20, this is achieved by remembering that the square root of 20 is the same thing as the square root of 4 times the square root of 5. Four is a perfect square that reduces to 2, but 5 is not a perfect square, resulting in the answer 2 times the square root of 5.

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