Solve frac{frac{sqrt{27}}{sqrt{3}}}{frac{sqrt{3}}{128}}

$$\frac { \frac { \sqrt { 27 } } { \sqrt { 3 } } } { \frac { \sqrt { 3 } } { 128 } }$$

Evaluate

$$128\sqrt{3}\approx 221.702503369$$

Solution Steps

Divide \frac{\sqrt{27}}{\sqrt{3}} by \frac{\sqrt{3}}{128} by multiplying \frac{\sqrt{27}}{\sqrt{3}} by the reciprocal of \frac{\sqrt{3}}{128}.

$$\frac{\sqrt{27}\times 128}{\sqrt{3}\sqrt{3}}$$

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}.

$$\frac{3\sqrt{3}\times 128}{\sqrt{3}\sqrt{3}}$$

Multiply 3 and 128 to get 384.

$$\frac{384\sqrt{3}}{\sqrt{3}\sqrt{3}}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{384\sqrt{3}}{3}$$

Divide 384\sqrt{3} by 3 to get 128\sqrt{3}.

$$128\sqrt{3}$$