SOLUTION: I need to simplify radical 176a^3b^5 but I am having trouble knowing exactly where to begin.

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Question 531015: I need to simplify radical 176a^3b^5 but I am having trouble knowing exactly where to begin.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28176%2Aa%5E3%2Ab%5E5%29 Start with the given expression.


sqrt%2816%2A11%2Aa%5E3%2Ab%5E5%29 Factor 176 into 16%2A11


sqrt%2816%2A11%2Aa%5E2%2Aa%2Ab%5E5%29 Factor a%5E3 into a%5E2%2Aa


sqrt%2816%2A11%2Aa%5E2%2Aa%2Ab%5E2%2Ab%5E2%2Ab%29 Factor b%5E5 into b%5E2%2Ab%5E2%2Ab


Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


Take the square root of 16 to get 4.


4%2Asqrt%2811%29%2Aa%2Asqrt%28a%29%2Asqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%29 Take the square root of a%5E2 to get a.


4%2Asqrt%2811%29%2Aa%2Asqrt%28a%29%2Ab%2Ab%2Asqrt%28b%29 Take the square root of b%5E2 to get b.


4ab%5E2%2Asqrt%2811ab%29 Rearrange and multiply the terms.

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Answer:


So sqrt%28176%2Aa%5E3%2Ab%5E5%29 simplifies to 4ab%5E2%2Asqrt%2811ab%29


In other words, sqrt%28176%2Aa%5E3%2Ab%5E5%29=4ab%5E2%2Asqrt%2811ab%29 where every variable is non-negative.