SOLUTION: use property 1 to simplify the following radical expressions. assume that all variables represent positive real numbers /72x^3

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Question 96818: use property 1 to simplify the following radical expressions. assume that all variables represent positive real numbers
/72x^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2872%2Ax%5E3%29Start with the given expression
sqrt%2836%2A2%2Ax%5E3%29 Factor 72 into 36%2A2

sqrt%2836%2A2%2Ax%2Ax%5E2%29 Factor x%5E3 into x%2Ax%5E2

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

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

6%2Asqrt%282%29%2Asqrt%28x%29%2Ax Take the square root of the perfect squares x%5E2 to get x

6%2Asqrt%282%29%2Ax%2Asqrt%28x%29 Multiply the common terms
6%2Ax%2Asqrt%28x%29%2Asqrt%282%29 Rearrange the terms
6%2Ax%2Asqrt%282x%29 Group the square root terms