SOLUTION: Could someone help me out here? I understand how to simplify sqrt(3/25) but how do you simplify; sqrt(a^2)/sqrt(b^5) or sqrt(a/b)sqrt(a^2)/(b^2)

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: Could someone help me out here? I understand how to simplify sqrt(3/25) but how do you simplify; sqrt(a^2)/sqrt(b^5) or sqrt(a/b)sqrt(a^2)/(b^2)       Log On

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Question 186777: Could someone help me out here?
I understand how to simplify sqrt(3/25) but how do you simplify;
sqrt(a^2)/sqrt(b^5)
or
sqrt(a/b)sqrt(a^2)/(b^2)
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28a%5E2%29%2Fsqrt%28b%5E5%29 Start with the given expression.


sqrt%28a%5E2%29%2Fsqrt%28b%5E2%2Ab%5E2%2Ab%29 Factor b%5E5 to get b%5E2%2Ab%5E2%2Ab


sqrt%28a%5E2%29%2F%28sqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%29%29 Break up the square root.


a%2F%28b%2Ab%2Asqrt%28b%29%29 Take the square root of a%5E2 to get 'a'. Take the square root of b%5E2 to get 'b'


a%2F%28b%5E2%2Asqrt%28b%29%29 Multiply


%28a%2Asqrt%28b%29%29%2F%28b%5E2%2Asqrt%28b%29%2Asqrt%28b%29%29 Multiply BOTH the numerator and denominator by sqrt%28b%29


%28a%2Asqrt%28b%29%29%2F%28b%5E2%2Ab%29 Multiply sqrt%28b%29 by itself to get 'b'


%28a%2Asqrt%28b%29%29%2F%28b%5E3%29 Multiply



So sqrt%28a%5E2%29%2Fsqrt%28b%5E5%29=%28a%2Asqrt%28b%29%29%2F%28b%5E3%29 where both 'a' and 'b' are positive.