Thread: How do I simplify this expression?

1. How do I simplify this expression?

250X^9y^5 all inside a 3rd root thing...
The answer is 5X^3 Y^3 and then a "2y^2" which is inside a square root thing.
Thanks a lot!

2. Originally Posted by hersheybar11

250X^9y^5 all inside a 3rd root thing...
The answer is 5X^3 Y^3 and then a "2y^2" which is inside a square root thing.
Thanks a lot!
$\sqrt[3]{250 x^9 y^5}$

Since that is a cube root, set everything into cubes as much as possible.

250= 125* 2 and 125= 5*5*5= $5^3$

$x^9= (x*x*x)(x*x*x)(x*x*x)= (x^3)^3$

$y^5= y*y*y*y*y= (y*y)(y*y*y)= y^2 y^3$

So what that is is $\sqrt[3]{2(5^3)(x^3)^3y^2y^3}$
Of course, the definition of "cube root" is that $\sqrt[3]{a^3}= a$.

$\sqrt[3]{250 x^9 y^5}= \sqrt[3]{2}\sqrt[3]{5^3}\sqrt[3]{(x^3)^3}\sqrt[3]{y^2}\sqrt[3]{y^3}$

$= \sqrt[3]{2}(5)(x^3)\sqrt[3]{y^2}y= 5x^3y\sqrt[3]{2y^2}$