What is the square root of 400

The short answer is \( \sqrt{ 400 } = 20 \).

If that's all you're looking for, thanks for coming by. But if you're interested in the hows and whys behind square roots, continue reading and we'll tell you all about the square root of 400.

400 is a perfect square

Let's look at some math.

$$ \LARGE \sqrt{ 400 } = 20 $$

The important part is to the right of the equals sign. Since the square root of 400 is a whole number, that means that 400 is a perfect square. The square root of 400 is 20, which is a whole number.

The next perfect square greater than 400 is 441. The previous perfect square less than 400 is 361.

Square root of 400 as an exponent

Any square root can be converted to a number with a fractional exponent. In the case of 400 the following two values are equal.

$$ \LARGE \sqrt{ 400 } = 400^{^1/_2} $$

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