How do you simplify sqrt(xyz)*sqrt(2y^3z^4)?

Oct 2, 2017

${y}^{2} {z}^{2} \sqrt{2 x z}$

Explanation:

$\sqrt{x y z} \cdot \sqrt{2 {y}^{3} {z}^{4}} \implies \sqrt{2 x {y}^{4} {z}^{5}}$

we can see this as:

sqrt(2 xx x xx y^4 xx z^4xxz

We can now extract any exact roots:

The $\sqrt{{y}^{4}} = {y}^{2}$ since ${y}^{2} \times {y}^{2} = {y}^{2 + 2} = {y}^{4}$

${y}^{2} \sqrt{2 \times x \times {z}^{4} \times z}$

Do the same for ${z}^{4}$:

${y}^{2} {z}^{2} \sqrt{2 \times x \times z}$

This is as far as we can go, so:

${y}^{2} {z}^{2} \sqrt{2 x z}$