SOLUTION: Simplify by factoring assume that all expressions under radicals are nonnegative numbers {{{(sqrt75a^2b)}}}

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Question 368855: Simplify by factoring assume that all expressions under radicals are nonnegative numbers
%28sqrt75a%5E2b%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2875%2Aa%5E2%2Ab%29 Start with the given expression.


sqrt%2825%2A3%2Aa%5E2%2Ab%29 Factor 75 into 25%2A3


sqrt%2825%29%2Asqrt%283%29%2Asqrt%28a%5E2%29%2Asqrt%28b%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


5%2Asqrt%283%29%2Asqrt%28a%5E2%29%2Asqrt%28b%29 Take the square root of 25 to get 5.


5%2Asqrt%283%29%2Aa%2Asqrt%28b%29 Take the square root of a%5E2 to get a.


5a%2Asqrt%283b%29 Rearrange and multiply the terms.

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Answer:


So sqrt%2875%2Aa%5E2%2Ab%29 simplifies to 5a%2Asqrt%283b%29


In other words, sqrt%2875%2Aa%5E2%2Ab%29=5a%2Asqrt%283b%29 where every variable is non-negative.


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Jim