What is the square root of 123

The short answer is \( \sqrt{ 123 } = 11.090536506409 \).

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 123.

123 is not a perfect square

Let's look at some math

$$ \LARGE \sqrt{ 123 } = 11.090536506409 $$

Note that \(11.090536506409\) is not a whole number, therefore 123 is not a perfect square.

The next perfect square greater than 123 is 144. The previous perfect square less than 123 is 121.

Square root of 123 as an exponent

Any square root can be converted to a number with a fractional exponent. In the case of 123 the following two values are equal.

$$ \LARGE \sqrt{ 123 } = 123^{^1/_2} $$

Square root of 123 as a fraction

Since 123 is not a perfect square, sometimes we might want to get a fractional estimate of the square root value. In the case of 123 that value is \(\Large 11 \frac{22}{243}\).

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