Solve frac{frac{3sqrt{3}}{10}}{10/4sqrt{5}}

$$\frac { \frac { 3 \sqrt { 3 } } { 10 } } { \frac { 10 } { 4 \sqrt { 5 } } }$$

Evaluate

$$\frac{3\sqrt{15}}{25}\approx 0.464758002$$

Solution Steps

Divide \frac{3\sqrt{3}}{10} by \frac{10}{4\sqrt{5}} by multiplying \frac{3\sqrt{3}}{10} by the reciprocal of \frac{10}{4\sqrt{5}}.

$$\frac{3\sqrt{3}\times 4\sqrt{5}}{10\times 10}$$

Cancel out 2\times 2 in both numerator and denominator.

$$\frac{3\sqrt{3}\sqrt{5}}{5\times 5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{3\sqrt{15}}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$\frac{3\sqrt{15}}{25}$$