Solve sqrt{24}*sqrt{6/5}

$$\sqrt { 24 } \times \sqrt { \frac { 6 } { 5 } }$$

Evaluate

$$\frac{12\sqrt{5}}{5}\approx 5.366563146$$

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}.

$$2\sqrt{6}\sqrt{\frac{6}{5}}$$

Rewrite the square root of the division \sqrt{\frac{6}{5}} as the division of square roots \frac{\sqrt{6}}{\sqrt{5}}.

$$2\sqrt{6}\times \frac{\sqrt{6}}{\sqrt{5}}$$

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

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

The square of \sqrt{5} is 5.

$$2\sqrt{6}\times \frac{\sqrt{6}\sqrt{5}}{5}$$

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

$$2\sqrt{6}\times \frac{\sqrt{30}}{5}$$

Express 2\times \frac{\sqrt{30}}{5} as a single fraction.

$$\frac{2\sqrt{30}}{5}\sqrt{6}$$

Express \frac{2\sqrt{30}}{5}\sqrt{6} as a single fraction.

$$\frac{2\sqrt{30}\sqrt{6}}{5}$$

Factor 30=6\times 5. Rewrite the square root of the product \sqrt{6\times 5} as the product of square roots \sqrt{6}\sqrt{5}.

$$\frac{2\sqrt{6}\sqrt{5}\sqrt{6}}{5}$$

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

$$\frac{2\times 6\sqrt{5}}{5}$$

Multiply 2 and 6 to get 12.

$$\frac{12\sqrt{5}}{5}$$