SOLUTION: The problem asks me to simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. √(32a^2 b)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The problem asks me to simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. √(32a^2 b)      Log On


   

Question 375104: The problem asks me to simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.
√(32a^2 b)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2832%2Aa%5E2%2Ab%29 Start with the given expression.


sqrt%2816%2A2%2Aa%5E2%2Ab%29 Factor 32 into 16%2A2


sqrt%2816%29%2Asqrt%282%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.


4%2Asqrt%282%29%2Asqrt%28a%5E2%29%2Asqrt%28b%29 Take the square root of 16 to get 4.


4%2Asqrt%282%29%2Aa%2Asqrt%28b%29 Take the square root of a%5E2 to get a.


4a%2Asqrt%282b%29 Recombine the roots and rearrange the terms.

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Answer:


So sqrt%2832%2Aa%5E2%2Ab%29 simplifies to 4a%2Asqrt%282b%29


In other words, sqrt%2832%2Aa%5E2%2Ab%29=4a%2Asqrt%282b%29 where every variable is non-negative.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim