Solve sqrt{(3/4-21/4-5)^2+1}

$$\sqrt { ( \frac { 3 } { 4 } - \frac { 21 } { 4 } - 5 ) ^ { 2 } + 1 }$$

Evaluate

$$\frac{\sqrt{365}}{2}\approx 9.552486587$$

Solution Steps

Subtract \frac{21}{4} from \frac{3}{4} to get -\frac{9}{2}.

$$\sqrt{\left(-\frac{9}{2}-5\right)^{2}+1}$$

Subtract 5 from -\frac{9}{2} to get -\frac{19}{2}.

$$\sqrt{\left(-\frac{19}{2}\right)^{2}+1}$$

Calculate -\frac{19}{2} to the power of 2 and get \frac{361}{4}.

$$\sqrt{\frac{361}{4}+1}$$

Add \frac{361}{4} and 1 to get \frac{365}{4}.

$$\sqrt{\frac{365}{4}}$$

Rewrite the square root of the division \sqrt{\frac{365}{4}} as the division of square roots \frac{\sqrt{365}}{\sqrt{4}}.

$$\frac{\sqrt{365}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{365}}{2}$$