Solve -sqrt{1-(frac{17sqrt{2}}{26})^2}=

$$- \sqrt { 1 - ( \frac { 17 \sqrt { 2 } } { 26 } ) ^ { 2 } } =$$

Evaluate

$$-\frac{7\sqrt{2}}{26}\approx -0.380749805$$

Solution Steps

To raise \frac{17\sqrt{2}}{26} to a power, raise both numerator and denominator to the power and then divide.

$$-\sqrt{1-\frac{\left(17\sqrt{2}\right)^{2}}{26^{2}}}$$

Expand \left(17\sqrt{2}\right)^{2}.

$$-\sqrt{1-\frac{17^{2}\left(\sqrt{2}\right)^{2}}{26^{2}}}$$

Calculate 17 to the power of 2 and get 289.

$$-\sqrt{1-\frac{289\left(\sqrt{2}\right)^{2}}{26^{2}}}$$

The square of \sqrt{2} is 2.

$$-\sqrt{1-\frac{289\times 2}{26^{2}}}$$

Multiply 289 and 2 to get 578.

$$-\sqrt{1-\frac{578}{26^{2}}}$$

Calculate 26 to the power of 2 and get 676.

$$-\sqrt{1-\frac{578}{676}}$$

Reduce the fraction \frac{578}{676} to lowest terms by extracting and canceling out 2.

$$-\sqrt{1-\frac{289}{338}}$$

Subtract \frac{289}{338} from 1 to get \frac{49}{338}.

$$-\sqrt{\frac{49}{338}}$$

Rewrite the square root of the division \sqrt{\frac{49}{338}} as the division of square roots \frac{\sqrt{49}}{\sqrt{338}}.

$$-\frac{\sqrt{49}}{\sqrt{338}}$$

Calculate the square root of 49 and get 7.

$$-\frac{7}{\sqrt{338}}$$

Factor 338=13^{2}\times 2. Rewrite the square root of the product \sqrt{13^{2}\times 2} as the product of square roots \sqrt{13^{2}}\sqrt{2}. Take the square root of 13^{2}.

$$-\frac{7}{13\sqrt{2}}$$

Rationalize the denominator of \frac{7}{13\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$-\frac{7\sqrt{2}}{13\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$-\frac{7\sqrt{2}}{13\times 2}$$

Multiply 13 and 2 to get 26.

$$-\frac{7\sqrt{2}}{26}$$