How do you simplify #\sqrt{\frac{75x^{14}}{81y^{2}}}#?

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Answer 1 · 2017-08-26T01:34:40

See a solution process below:

First, rewrite the expression as:

#sqrt((75x^14)/(81y^2)) => sqrt(75x^14)/sqrt(81y^2)#

We can now simplify the denominator as:

#sqrt(75x^14)/sqrt(81y^2) => sqrt(75x^14)/(9y)#

Now we can rewrite and simplify the numerator as:

#sqrt(75x^14)/(9y) => sqrt(25x^14 * 3)/(9y) => (sqrt(25x^14) * sqrt(3))/(9y) =>#

#(sqrt(25x^14) * sqrt(3))/(9y) => (5x^7 * sqrt(3))/(9y) =>#

#(5x^7sqrt(3))/(9y)#