SOLUTION: Rationalize the denominator. - root 245x^3/y^5

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Question 201162: Rationalize the denominator.
- root 245x^3/y^5
Answer by jsmallt9(3296) About Me  (Show Source):
You can put this solution on YOUR website!
I assume the problem is to rationalize -sqrt%28245x%5E3%2F%28y%5E5%29%29
If this is correct, then the denominator of fraction needs to be a perfect square. Since a variable raised to an even power is a perfect square, the current denominator, y^5, is not a perfect square. The simplest way to make the exponent on y even is to multiply y^5 by y which results in y^6.
The only valid way to multiply the denominator by y is to multiply the numerator by y, also:
-sqrt%28%28245x%5E3%2Fy%5E5%29%2A%28y%2Fy%29%29
which results in:
-sqrt%28245x%5E3y%2Fy%5E6%29%29
Now you can split the square root of the fraction into a fraction of square roots:
-%28sqrt%28245x%5E3y%29%2Fsqrt%28y%5E6%29%29
The denominator, sqrt%28y%5E6%29, will simplify to y^3 making the answer:
-%28sqrt%28245x%5E3y%29%2F%28y%5E3%29%29