Multiply and simplify. Assume that no radicands were formed by raising negative numbers to even powers.

Question

√6x^3 * √18x^2 =
√2 * 3 * x^3 * √2 * 3^2 * x^2 =
√2 * 3x^2x * √2 * 3^2 * x^2 =
6x^2 * √3x

Is this correct?? If not can you show me the correct steps? Please and thank you.

Answer 1

I assume you meant:
√(6x^3) * √(18x^2)

= √(108x^5)
= √36*√3*√x^4*√x
= 6*√3*x^2*√x
= 6√(3x)x^2
= 6x^2√(3x)

I don't know how you fudged that answer looking at your second line, which is totally wrong

it should be
√2 * √3 * √x^3 * √2 * √9 * √x^2
then
= √6 * x√x * √2 * 3 * x
= 3√12 * x^2√x
= 3*√4*√3 * x^2 * √x
= 6√(3x) x^2 or
= 6x^2 √(3x)