Solve 2*sqrt{frac{7/4}*3/4}{3frac{sqrt{7}}{8}}

$$\frac{ 2 \times \sqrt{ \frac{ 7 }{ 4 } } \times \frac{ 3 }{ 4 } }{ 3 \frac{ \sqrt{ 7 } }{ 8 } }$$

Evaluate

$$2$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{7}{4}} as the division of square roots \frac{\sqrt{7}}{\sqrt{4}}.

$$\frac{2\times \frac{\sqrt{7}}{\sqrt{4}}\times \frac{3}{4}}{3\times \frac{\sqrt{7}}{8}}$$

Calculate the square root of 4 and get 2.

$$\frac{2\times \frac{\sqrt{7}}{2}\times \frac{3}{4}}{3\times \frac{\sqrt{7}}{8}}$$

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{\frac{2\times 3}{4}\times \frac{\sqrt{7}}{2}}{3\times \frac{\sqrt{7}}{8}}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{6}{4}\times \frac{\sqrt{7}}{2}}{3\times \frac{\sqrt{7}}{8}}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{2}\times \frac{\sqrt{7}}{2}}{3\times \frac{\sqrt{7}}{8}}$$

Multiply \frac{3}{2} times \frac{\sqrt{7}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\sqrt{7}}{2\times 2}}{3\times \frac{\sqrt{7}}{8}}$$

Express 3\times \frac{\sqrt{7}}{8} as a single fraction.

$$\frac{\frac{3\sqrt{7}}{2\times 2}}{\frac{3\sqrt{7}}{8}}$$

Divide \frac{3\sqrt{7}}{2\times 2} by \frac{3\sqrt{7}}{8} by multiplying \frac{3\sqrt{7}}{2\times 2} by the reciprocal of \frac{3\sqrt{7}}{8}.

$$\frac{3\sqrt{7}\times 8}{2\times 2\times 3\sqrt{7}}$$

Cancel out 2\times 2\times 3\sqrt{7} in both numerator and denominator.

$$2$$

Factor

$$2$$