# What is the square root of 413

The short answer is $$\sqrt{ 413 } = 20.322401432902$$.

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 413.

## 413 is not a perfect square

Let's look at some math

$$\LARGE \sqrt{ 413 } = 20.322401432902$$

Note that $$20.322401432902$$ is not a whole number, therefore 413 is not a perfect square.

The next perfect square greater than 413 is 441. The previous perfect square less than 413 is 400.

## Square root of 413 as an exponent

Any square root can be converted to a number with a fractional exponent. In the case of 413 the following two values are equal.

$$\LARGE \sqrt{ 413 } = 413^{^1/_2}$$

## Square root of 413 as a fraction

Since 413 is not a perfect square, sometimes we might want to get a fractional estimate of the square root value. In the case of 413 that value is $$\Large 20 \frac{10}{31}$$.

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