What is the square root of 163

The short answer is \( \sqrt{ 163 } = 12.767145334804 \).

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 163.

163 is not a perfect square

Let's look at some math

$$ \LARGE \sqrt{ 163 } = 12.767145334804 $$

Note that \(12.767145334804\) is not a whole number, therefore 163 is not a perfect square.

The next perfect square greater than 163 is 169. The previous perfect square less than 163 is 144.

Square root of 163 as an exponent

Any square root can be converted to a number with a fractional exponent. In the case of 163 the following two values are equal.

$$ \LARGE \sqrt{ 163 } = 163^{^1/_2} $$

Square root of 163 as a fraction

Since 163 is not a perfect square, sometimes we might want to get a fractional estimate of the square root value. In the case of 163 that value is \(\Large 12 \frac{23}{30}\).

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