Solve sqrt{(2/5+7/2)^2-(7/2)^2}

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

Evaluate

$$\frac{\sqrt{74}}{5}\approx 1.720465053$$

Solution Steps

Add \frac{2}{5} and \frac{7}{2} to get \frac{39}{10}.

$$\sqrt{\left(\frac{39}{10}\right)^{2}-\left(\frac{7}{2}\right)^{2}}$$

Calculate \frac{39}{10} to the power of 2 and get \frac{1521}{100}.

$$\sqrt{\frac{1521}{100}-\left(\frac{7}{2}\right)^{2}}$$

Calculate \frac{7}{2} to the power of 2 and get \frac{49}{4}.

$$\sqrt{\frac{1521}{100}-\frac{49}{4}}$$

Subtract \frac{49}{4} from \frac{1521}{100} to get \frac{74}{25}.

$$\sqrt{\frac{74}{25}}$$

Rewrite the square root of the division \sqrt{\frac{74}{25}} as the division of square roots \frac{\sqrt{74}}{\sqrt{25}}.

$$\frac{\sqrt{74}}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$\frac{\sqrt{74}}{5}$$