SOLUTION: Please help with radical 12x^3/5. \/12x^3/5 The entire equation is under the radical sign.

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Question 54715: Please help with radical 12x^3/5. \/12x^3/5 The entire equation is under the radical sign.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28%2812x%5E3%29%2F5%29
`
Break everything into prime factors
`
sqrt%28%28%282%29%282%29%283%29%28x%29%28x%29%28x%29%29%2F5%29
`
Write (2)·(2) as (2)² and (x)·(x) as (x)²
`
sqrt%28%28%282%29%5E2%283%29%28x%29%5E2%28x%29%29%2F5%29
`
Take the (2)² out in front of the radical as just 2
Take the (x)² out in front of the radical as just |x|
`
2abs%28x%29sqrt%28%28%283%29%28x%29%29%2F5%29
`
Rationalize the denominator by multiplying under the
radical by 5/5:
`
2abs%28x%29sqrt%28%28%28%283%29%28x%29%29%2F5%29%285%2F5%29%29
`
OR
`
2abs%28x%29sqrt%28++%28%2815%29%28x%29%29%2F%28%285%29%285%29%29++%29
`
Write the (5)·(5) as (5)²
`
2abs%28x%29sqrt%28++%28%2815%29%28x%29%29%2F%28%285%29%5E2%29++%29
`
Take (5)² out in front of the radical as 5, and
since it came from the bottom, put it under the 2|x|.
The absolute value bars are necessary because the original
problem is a square root and even root radicals may never
represent a negative number, so we need absolute
values around the x in case x turned out to be
negative.
`
%282abs%28x%29%2F5%29sqrt%28++%2815%29%28x%29++%29
`
This can be written as
`
++%282abs%28x%29sqrt%28++15x++%29%29%2F5
`
Edwin