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\sqrt{\frac{3\times 10}{4}}
Express \frac{3}{4}\times 10 as a single fraction.
\sqrt{\frac{30}{4}}
Multiply 3 and 10 to get 30.
\sqrt{\frac{15}{2}}
Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.
\frac{\sqrt{15}}{\sqrt{2}}
Rewrite the square root of the division \sqrt{\frac{15}{2}} as the division of square roots \frac{\sqrt{15}}{\sqrt{2}}.
\frac{\sqrt{15}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}
Rationalize the denominator of \frac{\sqrt{15}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.
\frac{\sqrt{15}\sqrt{2}}{2}
The square of \sqrt{2} is 2.
\frac{\sqrt{30}}{2}
To multiply \sqrt{15} and \sqrt{2}, multiply the numbers under the square root.