Solve 1-(frac{4sqrt{2}}{9})^2

$$1 - ( \frac { 4 \sqrt { 2 } } { 9 } ) ^ { 2 }$$

Evaluate

$$\frac{49}{81}\approx 0.604938272$$

Solution Steps

To raise \frac{4\sqrt{2}}{9} to a power, raise both numerator and denominator to the power and then divide.

$$1-\frac{\left(4\sqrt{2}\right)^{2}}{9^{2}}$$

Expand \left(4\sqrt{2}\right)^{2}.

$$1-\frac{4^{2}\left(\sqrt{2}\right)^{2}}{9^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$1-\frac{16\left(\sqrt{2}\right)^{2}}{9^{2}}$$

The square of \sqrt{2} is 2.

$$1-\frac{16\times 2}{9^{2}}$$

Multiply 16 and 2 to get 32.

$$1-\frac{32}{9^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$1-\frac{32}{81}$$

Subtract \frac{32}{81} from 1 to get \frac{49}{81}.

$$\frac{49}{81}$$

Factor

$$\frac{7 ^ {2}}{3 ^ {4}} = 0.6049382716049383$$