Question

How do you simplify `sqrt(-225x^8)`?

Answer 1

By exponential rules, we know that `a^(n/m)=root(m)(a^n)`

Thus,

`sqrt(-225x^8)=root(2)(-225^1*x^8)=(-225^(1/2))(x^(8/2))=x^4sqrt(-(15^(2)))`

On the Real number's domain, this would be your final answer.

Considering imaginary numbers,

we have that `i^2=-1` and, thus, `sqrt(-1)=i`

`x^4sqrt((-1)(15^2))=x^4sqrt(-1)sqrt(15^2)=color(green)(15ix^4)`