SOLUTION: please help solve in steps. square root of 54a5b7

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Question 187246: please help solve in steps.
square root of 54a5b7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2854%2Aa%5E5%2Ab%5E7%29 Start with the given expression.


sqrt%289%2A6%2Aa%5E5%2Ab%5E7%29 Factor 54 into 9%2A6


sqrt%289%2A6%2Aa%5E2%2Aa%5E2%2Aa%2Ab%5E7%29 Factor a%5E5 into a%5E2%2Aa%5E2%2Aa


sqrt%289%2A6%2Aa%5E2%2Aa%5E2%2Aa%2Ab%5E2%2Ab%5E2%2Ab%5E2%2Ab%29 Factor b%5E7 into b%5E2%2Ab%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 9 to get 3.


Take the square root of a%5E2 to get a.


3%2Asqrt%286%29%2Aa%2Aa%2Asqrt%28a%29%2Ab%2Ab%2Ab%2Asqrt%28b%29 Take the square root of b%5E2 to get b.


3a%5E2b%5E3%2Asqrt%286ab%29 Rearrange and combine the terms.

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Answer:


So sqrt%2854%2Aa%5E5%2Ab%5E7%29 simplifies to 3a%5E2b%5E3%2Asqrt%286ab%29


In other words, sqrt%2854%2Aa%5E5%2Ab%5E7%29=3a%5E2b%5E3%2Asqrt%286ab%29 where every variable is nonnegative.