Solve sqrt{(4-(-8))^2+(1/2-9)^2}=

$$\sqrt { ( 4 - ( - 8 ) ) ^ { 2 } + ( \frac { 1 } { 2 } - 9 ) ^ { 2 } } =$$

Evaluate

$$\frac{\sqrt{865}}{2}\approx 14.70544117$$

Solution Steps

The opposite of -8 is 8.

$$\sqrt{\left(4+8\right)^{2}+\left(\frac{1}{2}-9\right)^{2}}$$

Add 4 and 8 to get 12.

$$\sqrt{12^{2}+\left(\frac{1}{2}-9\right)^{2}}$$

Calculate 12 to the power of 2 and get 144.

$$\sqrt{144+\left(\frac{1}{2}-9\right)^{2}}$$

Subtract 9 from \frac{1}{2} to get -\frac{17}{2}.

$$\sqrt{144+\left(-\frac{17}{2}\right)^{2}}$$

Calculate -\frac{17}{2} to the power of 2 and get \frac{289}{4}.

$$\sqrt{144+\frac{289}{4}}$$

Add 144 and \frac{289}{4} to get \frac{865}{4}.

$$\sqrt{\frac{865}{4}}$$

Rewrite the square root of the division \sqrt{\frac{865}{4}} as the division of square roots \frac{\sqrt{865}}{\sqrt{4}}.

$$\frac{\sqrt{865}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{865}}{2}$$