Solve sqrt{14^2+[5/2]^2}

$$\sqrt { 14 ^ { 2 } + [ \frac { 5 } { 2 } ] ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{809}}{2}\approx 14.221462653$$

Solution Steps

Calculate 14 to the power of 2 and get 196.

$$\sqrt{196+\left(\frac{5}{2}\right)^{2}}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\sqrt{196+\frac{25}{4}}$$

Convert 196 to fraction \frac{784}{4}.

$$\sqrt{\frac{784}{4}+\frac{25}{4}}$$

Since \frac{784}{4} and \frac{25}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{784+25}{4}}$$

Add 784 and 25 to get 809.

$$\sqrt{\frac{809}{4}}$$

Rewrite the square root of the division \sqrt{\frac{809}{4}} as the division of square roots \frac{\sqrt{809}}{\sqrt{4}}.

$$\frac{\sqrt{809}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{809}}{2}$$