Solve sqrt{36/2+9^2/2}

$$\sqrt { \frac { 36 } { 2 } + \frac { 9 ^ { 2 } } { 2 } }$$

Evaluate

$$\frac{3\sqrt{26}}{2}\approx 7.64852927$$

Solution Steps

Divide 36 by 2 to get 18.

$$\sqrt{18+\frac{9^{2}}{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\sqrt{18+\frac{81}{2}}$$

Convert 18 to fraction \frac{36}{2}.

$$\sqrt{\frac{36}{2}+\frac{81}{2}}$$

Since \frac{36}{2} and \frac{81}{2} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{36+81}{2}}$$

Add 36 and 81 to get 117.

$$\sqrt{\frac{117}{2}}$$

Rewrite the square root of the division \sqrt{\frac{117}{2}} as the division of square roots \frac{\sqrt{117}}{\sqrt{2}}.

$$\frac{\sqrt{117}}{\sqrt{2}}$$

Factor 117=3^{2}\times 13. Rewrite the square root of the product \sqrt{3^{2}\times 13} as the product of square roots \sqrt{3^{2}}\sqrt{13}. Take the square root of 3^{2}.

$$\frac{3\sqrt{13}}{\sqrt{2}}$$

Rationalize the denominator of \frac{3\sqrt{13}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{13}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{13}\sqrt{2}}{2}$$

To multiply \sqrt{13} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{3\sqrt{26}}{2}$$