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\frac{5\sqrt{3}}{\sqrt{8}}
Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.
\frac{5\sqrt{3}}{2\sqrt{2}}
Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.
\frac{5\sqrt{3}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}
Rationalize the denominator of \frac{5\sqrt{3}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.
\frac{5\sqrt{3}\sqrt{2}}{2\times 2}
The square of \sqrt{2} is 2.
\frac{5\sqrt{6}}{2\times 2}
To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.
\frac{5\sqrt{6}}{4}
Multiply 2 and 2 to get 4.