SOLUTION: If p > 0, which of the following is equal to √48p^3 A. 4p√3p B. 3p√4p C. 2√12p D. 3√8p E. 16p√3p Please Help me what to do step by step.

Algebra ->  Test -> SOLUTION: If p > 0, which of the following is equal to √48p^3 A. 4p√3p B. 3p√4p C. 2√12p D. 3√8p E. 16p√3p Please Help me what to do step by step.      Log On


   

Question 282541: If p > 0, which of the following is equal to √48p^3
A. 4p√3p
B. 3p√4p
C. 2√12p
D. 3√8p
E. 16p√3p
Please Help me what to do step by step.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2848%2Ap%5E3%29 Start with the given expression.


sqrt%2816%2A3%2Ap%5E3%29 Factor 48 into 16%2A3


sqrt%2816%2A3%2Ap%5E2%2Ap%29 Factor p%5E3 into p%5E2%2Ap


sqrt%2816%29%2Asqrt%283%29%2Asqrt%28p%5E2%29%2Asqrt%28p%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


4%2Asqrt%283%29%2Asqrt%28p%5E2%29%2Asqrt%28p%29 Take the square root of 16 to get 4.


4%2Asqrt%283%29%2Ap%2Asqrt%28p%29 Take the square root of p%5E2 to get p.


4p%2Asqrt%283p%29 Rearrange and multiply the terms.

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Answer:


So sqrt%2848%2Ap%5E3%29 simplifies to 4p%2Asqrt%283p%29


In other words, sqrt%2848%2Ap%5E3%29=4p%2Asqrt%283p%29 where p%3E=0