Solve sqrt{8}*sqrt{2/3}

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

Evaluate

$$\frac{4\sqrt{3}}{3}\approx 2.309401077$$

Solution Steps

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}.

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

Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

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

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

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

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

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{3}}{3}$$