SOLUTION: How would I go about solving a problem such as: √27a^2b^3 I remember doing this last year, but I forgot the steps to simplifying it.

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Question 209787: How would I go about solving a problem such as: √27a^2b^3 I remember doing this last year, but I forgot the steps to simplifying it.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2827%2Aa%5E2%2Ab%5E3%29 Start with the given expression.


sqrt%289%2A3%2Aa%5E2%2Ab%5E3%29 Factor 27 into 9%2A3


sqrt%289%2A3%2Aa%5E2%2Ab%5E2%2Ab%29 Factor b%5E3 into b%5E2%2Ab


sqrt%289%29%2Asqrt%283%29%2Asqrt%28a%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


3%2Asqrt%283%29%2Asqrt%28a%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%29 Take the square root of 9 to get 3.


3%2Asqrt%283%29%2Aa%2Asqrt%28b%5E2%29%2Asqrt%28b%29 Take the square root of a%5E2 to get a.


3%2Asqrt%283%29%2Aa%2Ab%2Asqrt%28b%29 Take the square root of b%5E2 to get b.


3ab%2Asqrt%283b%29 Rearrange and multiply the terms.

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Answer:


So sqrt%2827%2Aa%5E2%2Ab%5E3%29 simplifies to 3ab%2Asqrt%283b%29


In other words, sqrt%2827%2Aa%5E2%2Ab%5E3%29=3ab%2Asqrt%283b%29 where every variable is non-negative.