Solve sqrt{1-(frac{7sqrt{5}}{27})^2}

$$\sqrt { 1 - ( \frac { 7 \sqrt { 5 } } { 27 } ) ^ { 2 } }$$

Evaluate

$$\frac{22}{27}\approx 0.814814815$$

Solution Steps

To raise \frac{7\sqrt{5}}{27} to a power, raise both numerator and denominator to the power and then divide.

$$\sqrt{1-\frac{\left(7\sqrt{5}\right)^{2}}{27^{2}}}$$

Expand \left(7\sqrt{5}\right)^{2}.

$$\sqrt{1-\frac{7^{2}\left(\sqrt{5}\right)^{2}}{27^{2}}}$$

Calculate 7 to the power of 2 and get 49.

$$\sqrt{1-\frac{49\left(\sqrt{5}\right)^{2}}{27^{2}}}$$

The square of \sqrt{5} is 5.

$$\sqrt{1-\frac{49\times 5}{27^{2}}}$$

Multiply 49 and 5 to get 245.

$$\sqrt{1-\frac{245}{27^{2}}}$$

Calculate 27 to the power of 2 and get 729.

$$\sqrt{1-\frac{245}{729}}$$

Subtract \frac{245}{729} from 1 to get \frac{484}{729}.

$$\sqrt{\frac{484}{729}}$$

Rewrite the square root of the division \frac{484}{729} as the division of square roots \frac{\sqrt{484}}{\sqrt{729}}. Take the square root of both numerator and denominator.

$$\frac{22}{27}$$

Factor

$$\frac{2 \cdot 11}{3 ^ {3}} = 0.8148148148148148$$