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\sqrt{\frac{3}{2}}
Anything divided by one gives itself.
\frac{\sqrt{3}}{\sqrt{2}}
Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.
\frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}
Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.
\frac{\sqrt{3}\sqrt{2}}{2}
The square of \sqrt{2} is 2.
\frac{\sqrt{6}}{2}
To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.