SOLUTION: Divide and simplify if possible √(250x^16)/√(2x)

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Question 970676: Divide and simplify if possible
√(250x^16)/√(2x)
Found 2 solutions by ankor@dixie-net.com, josgarithmetic:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Divide and simplify if possible
sqrt%28250x%5E16%29%2Fsqrt%282x%29
:
sqrt%28%28250x%5E16%29%2F%282x%29%29
cancel 2x
sqrt%28125x%5E15%29
factor inside the radical to reveal perfect squares
sqrt%2825%2A5%2Ax%5E14%2Ax%29
Extract the squares
5x%5E7%2Asqrt%285x%29

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%285%5E2%2A10%2Ax%5E8%2Ax%5E8%29%2Fsqrt%282x%29

5%2Ax%5E8%2Asqrt%282%2A5%29%2F%28sqrt%282%29%2Asqrt%28x%29%29

5%2Ax%5E8%2Asqrt%282%29sqrt%285%29%2F%28sqrt%282%29%28sqrt%28x%29%29%29

%285%2Ax%5E8%2Asqrt%285%29%29%2F%28sqrt%28x%29%29

Next you can rationalize the denominator:

%28%285%2Ax%5E8%2Asqrt%285%29%29%2F%28sqrt%28x%29%29%29%28sqrt%28x%29%2Fsqrt%28x%29%29

%285%2Ax%5E8%2Asqrt%28x%29sqrt%285%29%29%2Fx

%285x%5E8%2Asqrt%285x%29%29%2Fx

highlight%285x%5E7%2Asqrt%285x%29%29