Solve frac{7/4sqrt{24}}{7/2}sqrt{6}

$$\frac{ \frac{ 7 }{ 4 } \sqrt{ 24 } }{ \frac{ 7 }{ 2 } } \sqrt{ 6 }$$

Evaluate

$$6$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

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

Express \frac{7}{4}\times 2 as a single fraction.

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

Multiply 7 and 2 to get 14.

$$\frac{\frac{14}{4}\sqrt{6}}{\frac{7}{2}}\sqrt{6}$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{7}{2}\sqrt{6}}{\frac{7}{2}}\sqrt{6}$$

Divide \frac{7}{2}\sqrt{6} by \frac{7}{2} by multiplying \frac{7}{2}\sqrt{6} by the reciprocal of \frac{7}{2}.

$$\frac{\frac{7}{2}\sqrt{6}\times 2}{7}\sqrt{6}$$

Cancel out 2 and 2.

$$\frac{7\sqrt{6}}{7}\sqrt{6}$$

Cancel out 7 and 7.

$$\sqrt{6}\sqrt{6}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$6$$

Factor

$$2\times 3$$