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

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

Evaluate

$$\frac{\sqrt{5}}{2}\approx 1.118033989$$

Solution Steps

Subtract 4 from 5 to get 1.

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

Calculate 1 to the power of 2 and get 1.

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

Subtract \frac{5}{2} from 3 to get \frac{1}{2}.

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

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

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

Add 1 and \frac{1}{4} to get \frac{5}{4}.

$$\sqrt{\frac{5}{4}}$$

Rewrite the square root of the division \sqrt{\frac{5}{4}} as the division of square roots \frac{\sqrt{5}}{\sqrt{4}}.

$$\frac{\sqrt{5}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{5}}{2}$$