SOLUTION: Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. {{{ sqrt( 12a^2b) }}}

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Question 197400: Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.
+sqrt%28+12a%5E2b%29+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2812%2Aa%5E2%2Ab%29 Start with the given expression.


sqrt%284%2A3%2Aa%5E2%2Ab%29 Factor 12 into 4%2A3


sqrt%284%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.


2%2Asqrt%283%29%2Asqrt%28a%5E2%29%2Asqrt%28b%29 Take the square root of 4 to get 2.


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


2a%2Asqrt%283b%29 Rearrange and multiply.

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Answer:


So sqrt%2812%2Aa%5E2%2Ab%29 simplifies to 2a%2Asqrt%283b%29


In other words, sqrt%2812%2Aa%5E2%2Ab%29=2a%2Asqrt%283b%29 where every variable is non-negative.