Solve sqrt{(9/2)^2+(15/2)^2}

$$\sqrt { ( \frac { 9 } { 2 } ) ^ { 2 } + ( \frac { 15 } { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{3\sqrt{34}}{2}\approx 8.746427842$$

Solution Steps

Calculate \frac{9}{2} to the power of 2 and get \frac{81}{4}.

$$\sqrt{\frac{81}{4}+\left(\frac{15}{2}\right)^{2}}$$

Calculate \frac{15}{2} to the power of 2 and get \frac{225}{4}.

$$\sqrt{\frac{81}{4}+\frac{225}{4}}$$

Since \frac{81}{4} and \frac{225}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{81+225}{4}}$$

Add 81 and 225 to get 306.

$$\sqrt{\frac{306}{4}}$$

Reduce the fraction \frac{306}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{153}{2}}$$

Rewrite the square root of the division \sqrt{\frac{153}{2}} as the division of square roots \frac{\sqrt{153}}{\sqrt{2}}.

$$\frac{\sqrt{153}}{\sqrt{2}}$$

Factor 153=3^{2}\times 17. Rewrite the square root of the product \sqrt{3^{2}\times 17} as the product of square roots \sqrt{3^{2}}\sqrt{17}. Take the square root of 3^{2}.

$$\frac{3\sqrt{17}}{\sqrt{2}}$$

Rationalize the denominator of \frac{3\sqrt{17}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{17}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{17}\sqrt{2}}{2}$$

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

$$\frac{3\sqrt{34}}{2}$$