SOLUTION: Help. I have not done this in ages. Write the following expression in simplified radical form.Assume that all variables represent positive real numbers. The square root of 48x^3

Algebra ->  Square-cubic-other-roots -> SOLUTION: Help. I have not done this in ages. Write the following expression in simplified radical form.Assume that all variables represent positive real numbers. The square root of 48x^3       Log On


   

Question 190643: Help. I have not done this in ages.
Write the following expression in simplified radical form.Assume that all variables represent positive real numbers.
The square root of 48x^3 y^2
thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2848%2Ax%5E3%2Ay%5E2%29 Start with the given expression.


sqrt%2816%2A3%2Ax%5E3%2Ay%5E2%29 Factor 48 into 16%2A3


sqrt%2816%2A3%2Ax%5E2%2Ax%2Ay%5E2%29 Factor x%5E3 into x%5E2%2Ax


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


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


4%2Asqrt%283%29%2Ax%2Asqrt%28x%29%2Asqrt%28y%5E2%29 Take the square root of x%5E2 to get x.


4%2Asqrt%283%29%2Ax%2Asqrt%28x%29%2Ay Take the square root of y%5E2 to get y.


4xy%2Asqrt%283x%29 Rearrange and combine the terms.

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Answer:


So sqrt%2848%2Ax%5E3%2Ay%5E2%29 simplifies to 4xy%2Asqrt%283x%29


In other words, sqrt%2848%2Ax%5E3%2Ay%5E2%29=4xy%2Asqrt%283x%29 where every variable is non-negative.