# How do you simplify sqrt(24 x^10 y^11)?

Aug 19, 2016

$2 {x}^{5} {y}^{5} \sqrt{6 y}$

#### Explanation:

Note that $24 \text{ " =" " 4xx6" "=" } {2}^{2} \times 6$ giving:

$\sqrt{{2}^{2} \times 6 {x}^{10} {y}^{11}}$

take the ${2}^{2}$ outside the square root.

$2 \sqrt{6 {x}^{10} {y}^{11}}$

Note that $\sqrt{{x}^{10}} \text{ } = \sqrt{{x}^{2} \times {x}^{2} \times {x}^{2} \times {x}^{2} \times {x}^{2}} = {x}^{5}$

Take all of the ${x}^{2}$ outside the square root.

$2 {x}^{5} \sqrt{6 {y}^{11}}$

Note that $\sqrt{{y}^{11}} \text{ " =" " sqrt((y^2)^5xxy)" " =" } {y}^{5} \sqrt{y}$

$2 {x}^{5} {y}^{5} \sqrt{6 y}$