Solve sqrt{(1/3-(-1/2))^2+(5-2)^2}

$$\sqrt { ( \frac { 1 } { 3 } - ( - \frac { 1 } { 2 } ) ) ^ { 2 } + ( 5 - 2 ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{349}}{6}\approx 3.113590282$$

Solution Steps

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\sqrt{\left(\frac{1}{3}+\frac{1}{2}\right)^{2}+\left(5-2\right)^{2}}$$

Add \frac{1}{3} and \frac{1}{2} to get \frac{5}{6}.

$$\sqrt{\left(\frac{5}{6}\right)^{2}+\left(5-2\right)^{2}}$$

Calculate \frac{5}{6} to the power of 2 and get \frac{25}{36}.

$$\sqrt{\frac{25}{36}+\left(5-2\right)^{2}}$$

Subtract 2 from 5 to get 3.

$$\sqrt{\frac{25}{36}+3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{\frac{25}{36}+9}$$

Add \frac{25}{36} and 9 to get \frac{349}{36}.

$$\sqrt{\frac{349}{36}}$$

Rewrite the square root of the division \sqrt{\frac{349}{36}} as the division of square roots \frac{\sqrt{349}}{\sqrt{36}}.

$$\frac{\sqrt{349}}{\sqrt{36}}$$

Calculate the square root of 36 and get 6.

$$\frac{\sqrt{349}}{6}$$