What is the square root of 72

The short answer is \( \sqrt{ 72 } = 8.4852813742386 \).

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 72.

72 is not a perfect square

Let's look at some math

$$ \LARGE \sqrt{ 72 } = 8.4852813742386 $$

Note that \(8.4852813742386\) is not a whole number, therefore 72 is not a perfect square.

The next perfect square greater than 72 is 81. The previous perfect square less than 72 is 64.

Square root of 72 as an exponent

Any square root can be converted to a number with a fractional exponent. In the case of 72 the following two values are equal.

$$ \LARGE \sqrt{ 72 } = 72^{^1/_2} $$

Square root of 72 as a fraction

Since 72 is not a perfect square, sometimes we might want to get a fractional estimate of the square root value. In the case of 72 that value is \(\Large 8 \frac{16}{33}\).

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