Question

Which expression is equivalent to 3 sqrt 27x^18

Answer 1

Assuming your original expression was 3√(27x¹⁸), the answer is 9x⁹√(3).

We split up the radicand into perfect squares.  Once we do, we take out the things that were squared:
$3\sqrt{27x^{18}} = 3\sqrt{3\times3\times3x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2} = 3*3*xxxxxxxxx\sqrt{3}$
$=9x^9\sqrt{3}$