# How do you solve sqrt(243x^8y^5)?

Mar 10, 2016

= 9 x^4 y^2sqrt ( 3y

#### Explanation:

sqrt (243 x^8 y^5

Simplifying $\sqrt{243}$ by prime factorisation:
$243 = 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 = {3}^{5}$

sqrt (243 x^8 y^5) = sqrt (color(green)(3^5) x^8 y^5

= sqrt (color(green)(3^4* 3) * x^8 * y^4 *y

( note: Square root , can also be called as second root , so in terms of fraction, second root is a half power color(blue)(1/2 )

so, $\sqrt{{3}^{4}} = {3}^{2}$, $\sqrt{{x}^{8}} = {x}^{4}$ and $\sqrt{{y}^{4}} = {y}^{2}$

sqrt (color(green)(3^4* 3) * x^8 * y^4 * y ) = 3^2 * x^4 * y^2sqrt (color(green)( 3) y

= 9 x^4 y^2sqrt ( 3 y