Solve 3/frac{2{sqrt{27}}}

$$\frac { 3 } { \frac { 2 } { \sqrt { 27 } } }$$

Evaluate

$$\frac{9\sqrt{3}}{2}\approx 7.794228634$$

Solution Steps

Divide 3 by \frac{2}{\sqrt{27}} by multiplying 3 by the reciprocal of \frac{2}{\sqrt{27}}.

$$\frac{3\sqrt{27}}{2}$$

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}.

$$\frac{3\times 3\sqrt{3}}{2}$$

Multiply 3 and 3 to get 9.

$$\frac{9\sqrt{3}}{2}$$