Solve sqrt{22/3}*sqrt{24}

$$\sqrt { 2 \frac { 2 } { 3 } } \times \sqrt { 24 }$$

Evaluate

$$8$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\sqrt{\frac{6+2}{3}}\sqrt{24}$$

Add 6 and 2 to get 8.

$$\sqrt{\frac{8}{3}}\sqrt{24}$$

Rewrite the square root of the division \sqrt{\frac{8}{3}} as the division of square roots \frac{\sqrt{8}}{\sqrt{3}}.

$$\frac{\sqrt{8}}{\sqrt{3}}\sqrt{24}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2\sqrt{2}}{\sqrt{3}}\sqrt{24}$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{24}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{2}\sqrt{3}}{3}\sqrt{24}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{2\sqrt{6}}{3}\sqrt{24}$$

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}.

$$\frac{2\sqrt{6}}{3}\times 2\sqrt{6}$$

Express \frac{2\sqrt{6}}{3}\times 2 as a single fraction.

$$\frac{2\sqrt{6}\times 2}{3}\sqrt{6}$$

Express \frac{2\sqrt{6}\times 2}{3}\sqrt{6} as a single fraction.

$$\frac{2\sqrt{6}\times 2\sqrt{6}}{3}$$

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

$$\frac{2\times 6\times 2}{3}$$

Multiply 2 and 6 to get 12.

$$\frac{12\times 2}{3}$$

Multiply 12 and 2 to get 24.

$$\frac{24}{3}$$

Divide 24 by 3 to get 8.

$$8$$

Factor

$$2^{3}$$