# What is the Square root of 21?

Oct 17, 2015

$21 = 3 \cdot 7$ has no square factors, so $\sqrt{21}$ cannot be simplified.

$\sqrt{21} \approx 4.58257569495584000658$ is an irrational number whose square is $21$.

#### Explanation:

$\sqrt{21} = \sqrt{3 \cdot 7}$ has no square factors that can be 'moved outside the square root sign'.

For example $\sqrt{12} = \sqrt{{2}^{2} \cdot 3} = \sqrt{{2}^{2}} \sqrt{3} = 2 \sqrt{3}$

So $\sqrt{21}$ cannot be simplified.

It cannot be expressed as a rational number (fraction), so the best we can do with normal notation is to either stick with $\sqrt{21}$ or give an approximation, such as $\sqrt{21} \approx 4.58$.