Solve =9/4sqrt{4}div(3/8sqrt{31/5})

$$= \frac { 9 } { 4 } \sqrt { 4 } \div ( \frac { 3 } { 8 } \sqrt { 3 \frac { 1 } { 5 } } )$$

Evaluate

$$3\sqrt{5}\approx 6.708203932$$

Solution Steps

Calculate the square root of 4 and get 2.

$$\frac{\frac{9}{4}\times 2}{\frac{3}{8}\sqrt{\frac{3\times 5+1}{5}}}$$

Express \frac{9}{4}\times 2 as a single fraction.

$$\frac{\frac{9\times 2}{4}}{\frac{3}{8}\sqrt{\frac{3\times 5+1}{5}}}$$

Multiply 9 and 2 to get 18.

$$\frac{\frac{18}{4}}{\frac{3}{8}\sqrt{\frac{3\times 5+1}{5}}}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{9}{2}}{\frac{3}{8}\sqrt{\frac{3\times 5+1}{5}}}$$

Multiply 3 and 5 to get 15.

$$\frac{\frac{9}{2}}{\frac{3}{8}\sqrt{\frac{15+1}{5}}}$$

Add 15 and 1 to get 16.

$$\frac{\frac{9}{2}}{\frac{3}{8}\sqrt{\frac{16}{5}}}$$

Rewrite the square root of the division \sqrt{\frac{16}{5}} as the division of square roots \frac{\sqrt{16}}{\sqrt{5}}.

$$\frac{\frac{9}{2}}{\frac{3}{8}\times \frac{\sqrt{16}}{\sqrt{5}}}$$

Calculate the square root of 16 and get 4.

$$\frac{\frac{9}{2}}{\frac{3}{8}\times \frac{4}{\sqrt{5}}}$$

Rationalize the denominator of \frac{4}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\frac{9}{2}}{\frac{3}{8}\times \frac{4\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$\frac{\frac{9}{2}}{\frac{3}{8}\times \frac{4\sqrt{5}}{5}}$$

Multiply \frac{3}{8} times \frac{4\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9}{2}}{\frac{3\times 4\sqrt{5}}{8\times 5}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{9}{2}}{\frac{3\sqrt{5}}{2\times 5}}$$

Divide \frac{9}{2} by \frac{3\sqrt{5}}{2\times 5} by multiplying \frac{9}{2} by the reciprocal of \frac{3\sqrt{5}}{2\times 5}.

$$\frac{9\times 2\times 5}{2\times 3\sqrt{5}}$$

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

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

Rationalize the denominator of \frac{3\times 5}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{3\times 5\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

Multiply 3 and 5 to get 15.

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

Divide 15\sqrt{5} by 5 to get 3\sqrt{5}.

$$3\sqrt{5}$$