Evaluate
\frac{8\sqrt{3}}{3}\approx 4.618802154
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3\sqrt{3}-\frac{1}{\sqrt{3}}
Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.
3\sqrt{3}-\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}
Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
3\sqrt{3}-\frac{\sqrt{3}}{3}
The square of \sqrt{3} is 3.
\frac{8}{3}\sqrt{3}
Combine 3\sqrt{3} and -\frac{\sqrt{3}}{3} to get \frac{8}{3}\sqrt{3}.
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