Question

What is the negative square root of $27$ ?

Answer 1

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

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

$-\sqrt{27}$is not a square root of $27$ which we call the negative square root of $27$

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

So

$-\sqrt{27}=-\sqrt{3^2.3}=-\sqrt{3^2}\sqrt{3}=-3\sqrt{3}$