Solve frac{3/2sqrt{3}}{frac{sqrt{30}}{10}}

$$\frac { \frac { 3 } { 2 } \sqrt { 3 } } { \frac { \sqrt { 30 } } { 10 } }$$

Evaluate

$$\frac{3\sqrt{10}}{2}\approx 4.74341649$$

Solution Steps

Divide \frac{3}{2}\sqrt{3} by \frac{\sqrt{30}}{10} by multiplying \frac{3}{2}\sqrt{3} by the reciprocal of \frac{\sqrt{30}}{10}.

$$\frac{\frac{3}{2}\sqrt{3}\times 10}{\sqrt{30}}$$

Express \frac{3}{2}\times 10 as a single fraction.

$$\frac{\frac{3\times 10}{2}\sqrt{3}}{\sqrt{30}}$$

Multiply 3 and 10 to get 30.

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

Divide 30 by 2 to get 15.

$$\frac{15\sqrt{3}}{\sqrt{30}}$$

Rationalize the denominator of \frac{15\sqrt{3}}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{15\sqrt{3}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{15\sqrt{3}\sqrt{30}}{30}$$

Factor 30=3\times 10. Rewrite the square root of the product \sqrt{3\times 10} as the product of square roots \sqrt{3}\sqrt{10}.

$$\frac{15\sqrt{3}\sqrt{3}\sqrt{10}}{30}$$

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

$$\frac{15\times 3\sqrt{10}}{30}$$

Multiply 15 and 3 to get 45.

$$\frac{45\sqrt{10}}{30}$$

Divide 45\sqrt{10} by 30 to get \frac{3}{2}\sqrt{10}.

$$\frac{3}{2}\sqrt{10}$$