Solve sqrt{4*2/9}

$$\sqrt { 4 \times \frac { 2 } { 9 } }$$

Evaluate

$$\frac{2\sqrt{2}}{3}\approx 0.942809042$$

Solution Steps

Express 4\times \frac{2}{9} as a single fraction.

$$\sqrt{\frac{4\times 2}{9}}$$

Multiply 4 and 2 to get 8.

$$\sqrt{\frac{8}{9}}$$

Rewrite the square root of the division \sqrt{\frac{8}{9}} as the division of square roots \frac{\sqrt{8}}{\sqrt{9}}.

$$\frac{\sqrt{8}}{\sqrt{9}}$$

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}.

$$\frac{2\sqrt{2}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

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