Solve sqrt{(2-1/2)^2+(0-2)^2}-sqrt{(2-2)^2+(0-1/2)^2}

$$\sqrt { ( 2 - \frac { 1 } { 2 } ) ^ { 2 } + ( 0 - 2 ) ^ { 2 } } - \sqrt { ( 2 - 2 ) ^ { 2 } + ( 0 - \frac { 1 } { 2 } ) ^ { 2 } }$$

Evaluate

$$2$$

Solution Steps

Subtract \frac{1}{2} from 2 to get \frac{3}{2}.

$$\sqrt{\left(\frac{3}{2}\right)^{2}+\left(0-2\right)^{2}}-\sqrt{\left(2-2\right)^{2}+\left(0-\frac{1}{2}\right)^{2}}$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\sqrt{\frac{9}{4}+\left(0-2\right)^{2}}-\sqrt{\left(2-2\right)^{2}+\left(0-\frac{1}{2}\right)^{2}}$$

Subtract 2 from 0 to get -2.

$$\sqrt{\frac{9}{4}+\left(-2\right)^{2}}-\sqrt{\left(2-2\right)^{2}+\left(0-\frac{1}{2}\right)^{2}}$$

Calculate -2 to the power of 2 and get 4.

$$\sqrt{\frac{9}{4}+4}-\sqrt{\left(2-2\right)^{2}+\left(0-\frac{1}{2}\right)^{2}}$$

Add \frac{9}{4} and 4 to get \frac{25}{4}.

$$\sqrt{\frac{25}{4}}-\sqrt{\left(2-2\right)^{2}+\left(0-\frac{1}{2}\right)^{2}}$$

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{5}{2}-\sqrt{\left(2-2\right)^{2}+\left(0-\frac{1}{2}\right)^{2}}$$

Subtract 2 from 2 to get 0.

$$\frac{5}{2}-\sqrt{0^{2}+\left(0-\frac{1}{2}\right)^{2}}$$

Calculate 0 to the power of 2 and get 0.

$$\frac{5}{2}-\sqrt{0+\left(0-\frac{1}{2}\right)^{2}}$$

Subtract \frac{1}{2} from 0 to get -\frac{1}{2}.

$$\frac{5}{2}-\sqrt{0+\left(-\frac{1}{2}\right)^{2}}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{5}{2}-\sqrt{0+\frac{1}{4}}$$

Add 0 and \frac{1}{4} to get \frac{1}{4}.

$$\frac{5}{2}-\sqrt{\frac{1}{4}}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{5}{2}-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{5}{2} to get 2.

$$2$$

Factor

$$2$$