SOLUTION: Simplify. This is all one square root. square root 3x/2

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Question 113881: Simplify. This is all one square root.
square root 3x/2
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283x%2F2%29 is what I think you mean.

Begin with the fact that sqrt%28a%2Fb%29=sqrt%28a%29%2Fsqrt%28b%29 for all real a, and real b so long as b%3C%3E0.

So, sqrt%283x%2F2%29=sqrt%283x%29%2Fsqrt%282%29

However, simplest form requires that you have no radicals in the denominator, so you have to perform a process called 'rationalizing the denominator.' To perform this process, you need to start with the ideas that a+%2A+1=a for all real a and a%2Fa=1 for all real a, a%3C%3E0. What we are going to do is multiply our expression by 1 in the form of sqrt%282%29%2Fsqrt%282%29.



And that is the simplest form for the given expression.

Hope that helps,
John