SOLUTION: Can you show me the steps to simplify this square root problem? Thank you! Square root of 72a^2b^3

Algebra ->  Square-cubic-other-roots -> SOLUTION: Can you show me the steps to simplify this square root problem? Thank you! Square root of 72a^2b^3      Log On


   

Question 91070: Can you show me the steps to simplify this square root problem? Thank you!
Square root of 72a^2b^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2872%2Aa%5E2b%5E3%29Start with the given expression
sqrt%2836%2A2%2Aa%5E2b%5E3%29 Factor 72 into 36%2A2

sqrt%2836%2A2%2Aa%5E2%2Ab%2Ab%5E2%29 Factor a%5E2b%5E3 into a%5E2%2Ab%2Ab%5E2

sqrt%2836%29%2Asqrt%282%29%2Asqrt%28a%5E2%29%2Asqrt%28b%29%2Asqrt%28b%5E2%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

6%2Asqrt%282%29%2Asqrt%28a%5E2%29%2Asqrt%28b%29%2Asqrt%28b%5E2%29 Take the square root of the perfect square 36 to get 6

6%2Asqrt%282%29%2Aa%2Asqrt%28b%29%2Ab Take the square root of the perfect squares a%5E2 and b%5E2 to get a and b

6%2Asqrt%282%29%2Aab%2Asqrt%28b%29 Multiply the common terms
6%2Aab%2Asqrt%28b%29%2Asqrt%282%29 Rearrange the terms
6%2Aab%2Asqrt%282b%29 Group the square root terms