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\frac{2\sqrt{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{\left(2\sqrt{5}+\sqrt{3}\right)\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}
Rationalize the denominator of \frac{2\sqrt{5}+\sqrt{3}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.
\frac{\left(2\sqrt{5}+\sqrt{3}\right)\sqrt{2}}{2\times 2}
The square of \sqrt{2} is 2.
\frac{\left(2\sqrt{5}+\sqrt{3}\right)\sqrt{2}}{4}
Multiply 2 and 2 to get 4.
\frac{2\sqrt{5}\sqrt{2}+\sqrt{3}\sqrt{2}}{4}
Use the distributive property to multiply 2\sqrt{5}+\sqrt{3} by \sqrt{2}.
\frac{2\sqrt{10}+\sqrt{3}\sqrt{2}}{4}
To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.
\frac{2\sqrt{10}+\sqrt{6}}{4}
To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.