Solve (frac{5sqrt{2}}{13})^2-1

$$( \frac { 5 \sqrt { 2 } } { 13 } ) ^ { 2 } - 1$$

Evaluate

$$-\frac{119}{169}\approx -0.704142012$$

Solution Steps

To raise \frac{5\sqrt{2}}{13} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5\sqrt{2}\right)^{2}}{13^{2}}-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{13^{2}}{13^{2}}.

$$\frac{\left(5\sqrt{2}\right)^{2}}{13^{2}}-\frac{13^{2}}{13^{2}}$$

Since \frac{\left(5\sqrt{2}\right)^{2}}{13^{2}} and \frac{13^{2}}{13^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(5\sqrt{2}\right)^{2}-13^{2}}{13^{2}}$$

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

$$\frac{5^{2}\left(\sqrt{2}\right)^{2}}{13^{2}}-1$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25\left(\sqrt{2}\right)^{2}}{13^{2}}-1$$

The square of \sqrt{2} is 2.

$$\frac{25\times 2}{13^{2}}-1$$

Multiply 25 and 2 to get 50.

$$\frac{50}{13^{2}}-1$$

Calculate 13 to the power of 2 and get 169.

$$\frac{50}{169}-1$$

Subtract 1 from \frac{50}{169} to get -\frac{119}{169}.

$$-\frac{119}{169}$$

Factor

$$-\frac{119}{169} = -0.7041420118343196$$