# What is the negative square root of 27?

Jul 14, 2015

The negative square root of $27$ is $- \sqrt{27} = - 3 \sqrt{3}$

#### Explanation:

${x}^{2} = 27$ has two solutions, which we call $\pm \sqrt{27}$

$\sqrt{27}$ denotes the positive square root.

$- \sqrt{27}$ is also a square root of $27$, which we call the negative square root of $27$

If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$.

So:

$- \sqrt{27} = - \sqrt{{3}^{2} \cdot 3} = - \sqrt{{3}^{2}} \sqrt{3} = - 3 \sqrt{3}$