Question

Square root of 3z times Square root of 6z^2

Answer 1

`3z√(2z)`

Explanation:

Before multiplying the two factors, we can simplify the second factor.

We know that
`√(x^2) = x`, so we can rewrite the second factor as:

`\begin{aligned} √(6z^2) &= √(6) \cdot √(z^2) \\ &= \sqrt6 \cdot z \\ &= z\sqrt6\end{aligned}`

Now, we can execute the multiplication. Remember that
`x \cdot x = x^(2)`.

`√(3z) \cdot z\sqrt6`

`= z√(z \cdot 3 \cdot 6)`

`= z√(z\cdot3^2 \cdot 2)`

`= \boxed{3z√(2z)}`