Solve 3/4sqrt{96/5}=

$$\frac { 3 } { 4 } \sqrt { \frac { 96 } { 5 } } =$$

Evaluate

$$\frac{3\sqrt{30}}{5}\approx 3.286335345$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{96}{5}} as the division of square roots \frac{\sqrt{96}}{\sqrt{5}}.

$$\frac{3}{4}\times \frac{\sqrt{96}}{\sqrt{5}}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$\frac{3}{4}\times \frac{4\sqrt{6}}{\sqrt{5}}$$

Rationalize the denominator of \frac{4\sqrt{6}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{3}{4}\times \frac{4\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{3}{4}\times \frac{4\sqrt{6}\sqrt{5}}{5}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{3}{4}\times \frac{4\sqrt{30}}{5}$$

Multiply \frac{3}{4} times \frac{4\sqrt{30}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 4\sqrt{30}}{4\times 5}$$

Cancel out 4 in both numerator and denominator.

$$\frac{3\sqrt{30}}{5}$$