Question

What is the negative square root of 27?

Answer 1

The negative square root of `27` is `-sqrt(27) = -3sqrt(3)`

Explanation:

`x^2=27` has two solutions, which we call `+-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 >= 0` then `sqrt(ab) = sqrt(a)sqrt(b)`.

So:

`-sqrt(27) = -sqrt(3^2*3)=-sqrt(3^2)sqrt(3) = -3sqrt(3)`