Evaluate
\frac{3\sqrt{2}}{2}\approx 2.121320344
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\frac{6}{6\sqrt{2}}+\frac{8}{\sqrt{32}}
Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.
\frac{6\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}+\frac{8}{\sqrt{32}}
Rationalize the denominator of \frac{6}{6\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.
\frac{6\sqrt{2}}{6\times 2}+\frac{8}{\sqrt{32}}
The square of \sqrt{2} is 2.
\frac{\sqrt{2}}{2}+\frac{8}{\sqrt{32}}
Cancel out 6 in both numerator and denominator.
\frac{\sqrt{2}}{2}+\frac{8}{4\sqrt{2}}
Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.
\frac{\sqrt{2}}{2}+\frac{8\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}
Rationalize the denominator of \frac{8}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.
\frac{\sqrt{2}}{2}+\frac{8\sqrt{2}}{4\times 2}
The square of \sqrt{2} is 2.
\frac{\sqrt{2}}{2}+\sqrt{2}
Cancel out 2\times 4 in both numerator and denominator.
\frac{3}{2}\sqrt{2}
Combine \frac{\sqrt{2}}{2} and \sqrt{2} to get \frac{3}{2}\sqrt{2}.
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