Solve sqrt{1-(-frac{11sqrt{170}}{170})^2}

$$\sqrt { 1 - ( - \frac { 11 \sqrt { 170 } } { 170 } ) ^ { 2 } }$$

Evaluate

$$\frac{7\sqrt{170}}{170}\approx 0.536875492$$

Solution Steps

Calculate -\frac{11\sqrt{170}}{170} to the power of 2 and get \left(\frac{11\sqrt{170}}{170}\right)^{2}.

$$\sqrt{1-\left(\frac{11\sqrt{170}}{170}\right)^{2}}$$

To raise \frac{11\sqrt{170}}{170} to a power, raise both numerator and denominator to the power and then divide.

$$\sqrt{1-\frac{\left(11\sqrt{170}\right)^{2}}{170^{2}}}$$

Expand \left(11\sqrt{170}\right)^{2}.

$$\sqrt{1-\frac{11^{2}\left(\sqrt{170}\right)^{2}}{170^{2}}}$$

Calculate 11 to the power of 2 and get 121.

$$\sqrt{1-\frac{121\left(\sqrt{170}\right)^{2}}{170^{2}}}$$

The square of \sqrt{170} is 170.

$$\sqrt{1-\frac{121\times 170}{170^{2}}}$$

Multiply 121 and 170 to get 20570.

$$\sqrt{1-\frac{20570}{170^{2}}}$$

Calculate 170 to the power of 2 and get 28900.

$$\sqrt{1-\frac{20570}{28900}}$$

Reduce the fraction \frac{20570}{28900} to lowest terms by extracting and canceling out 170.

$$\sqrt{1-\frac{121}{170}}$$

Subtract \frac{121}{170} from 1 to get \frac{49}{170}.

$$\sqrt{\frac{49}{170}}$$

Rewrite the square root of the division \sqrt{\frac{49}{170}} as the division of square roots \frac{\sqrt{49}}{\sqrt{170}}.

$$\frac{\sqrt{49}}{\sqrt{170}}$$

Calculate the square root of 49 and get 7.

$$\frac{7}{\sqrt{170}}$$

Rationalize the denominator of \frac{7}{\sqrt{170}} by multiplying numerator and denominator by \sqrt{170}.

$$\frac{7\sqrt{170}}{\left(\sqrt{170}\right)^{2}}$$

The square of \sqrt{170} is 170.

$$\frac{7\sqrt{170}}{170}$$