Solve frac{3sqrt{2}}{4}*4/sqrt{30}

$$\frac { 3 \sqrt { 2 } } { 4 } \times \frac { 4 } { \sqrt { 30 } }$$

Evaluate

$$\frac{\sqrt{15}}{5}\approx 0.774596669$$

Solution Steps

Rationalize the denominator of \frac{4}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{3\sqrt{2}}{4}\times \frac{4\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{3\sqrt{2}}{4}\times \frac{4\sqrt{30}}{30}$$

Divide 4\sqrt{30} by 30 to get \frac{2}{15}\sqrt{30}.

$$\frac{3\sqrt{2}}{4}\times \frac{2}{15}\sqrt{30}$$

Multiply \frac{3\sqrt{2}}{4} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{2}\times 2}{4\times 15}\sqrt{30}$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{\sqrt{2}}{2\times 5}\sqrt{30}$$

Express \frac{\sqrt{2}}{2\times 5}\sqrt{30} as a single fraction.

$$\frac{\sqrt{2}\sqrt{30}}{2\times 5}$$

Factor 30=2\times 15. Rewrite the square root of the product \sqrt{2\times 15} as the product of square roots \sqrt{2}\sqrt{15}.

$$\frac{\sqrt{2}\sqrt{2}\sqrt{15}}{2\times 5}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{2\sqrt{15}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{2\sqrt{15}}{10}$$

Divide 2\sqrt{15} by 10 to get \frac{1}{5}\sqrt{15}.

$$\frac{1}{5}\sqrt{15}$$