# How do you simplify 4sqrt(8x^8y^6z^5) times 4sqrt(2x^2y^2z) ?

Mar 27, 2018

$64 {x}^{5} {y}^{4} {z}^{3}$

#### Explanation:

You can simplify each root as far as possible and then multiply the answers.

Or you can multiply the two roots together first and then find the square root of the product. I will follow the second option.

$4 \sqrt{8 {x}^{8} {y}^{6} {z}^{5}} \times 4 \sqrt{2 {x}^{2} {y}^{2} z}$

$= 4 \times 4 \sqrt{8 {x}^{8} {y}^{6} {z}^{5} \times 2 {x}^{2} {y}^{2} z}$

$= 16 \sqrt{16 {x}^{10} {y}^{8} {z}^{6}}$

$= 16 \times 4 {x}^{5} {y}^{4} {z}^{3} \text{ } \leftarrow$ divide the indices by $2$

$= 64 {x}^{5} {y}^{4} {z}^{3}$