How do you simplify #\frac{1}{2}x(\sqrt{\frac{3}{2}}x)#?

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Answer 1 · 2018-01-02T13:57:58

See a solution process below:

First, we can rewrite the expression as:

#(1/2 * sqrt(3/2))(x * x) =>#

#(1/2 * sqrt(3)/sqrt(2))(x^2) =>#

#(sqrt(3)/(2sqrt(2)))x^2#

We can now rationalize the denominator by multiplying the expression by the appropriate version of #1#:

#(sqrt(2)/sqrt(2) xx sqrt(3)/(2sqrt(2)))x^2 =>#

#(sqrt(2) xx sqrt(3))/(2sqrt(2) xx sqrt(2))x^2 =>#

#sqrt(2 xx 3)/(2sqrt(2)^2)x^2 =>#

#sqrt(6)/(2 xx 2)x^2 =>#

#sqrt(6)/4x^2#