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

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

Evaluate

$$\frac{\sqrt{34}}{2}\approx 2.915475947$$

Solution Steps

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

$$\sqrt{\frac{25}{4}+\left(-\frac{3}{2}\right)^{2}}$$

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

$$\sqrt{\frac{25}{4}+\frac{9}{4}}$$

Since \frac{25}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{25+9}{4}}$$

Add 25 and 9 to get 34.

$$\sqrt{\frac{34}{4}}$$

Reduce the fraction \frac{34}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{17}{2}}$$

Rewrite the square root of the division \sqrt{\frac{17}{2}} as the division of square roots \frac{\sqrt{17}}{\sqrt{2}}.

$$\frac{\sqrt{17}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{17}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{\sqrt{17}\sqrt{2}}{2}$$

To multiply \sqrt{17} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{34}}{2}$$