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

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Answer 1 · 2016-03-10T15:45:41

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

$sqrt (243 x^8 y^5$

Simplifying $sqrt243$ by prime factorisation:
$243 = 3*3*3*3*3 = 3^5$

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

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

( 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 $sqrt(y^4) = y^2$

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

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

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