Solve 2(frac{sqrt{2}}{3})^2

$$2 ( \frac { \sqrt { 2 } } { 3 } ) ^ { 2 }$$

Evaluate

$$\frac{4}{9}\approx 0.444444444$$

Solution Steps

To raise \frac{\sqrt{2}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

Express 2\times \frac{\left(\sqrt{2}\right)^{2}}{3^{2}} as a single fraction.

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

$$\frac{4}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4}{9}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2}} = 0.4444444444444444$$