Solve frac{sqrt{7}+sqrt{6}}{2pisqrt{6}}

$$\frac { \sqrt { 7 } + \sqrt { 6 } } { 2 \pi \sqrt { 6 } }$$

Evaluate

$$\frac{\sqrt{42}+6}{12\pi }\approx 0.331061929$$

Short Solution Steps

Rationalize the denominator of \frac{\sqrt{7}+\sqrt{6}}{2\pi \sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\left(\sqrt{7}+\sqrt{6}\right)\sqrt{6}}{2\pi \left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\left(\sqrt{7}+\sqrt{6}\right)\sqrt{6}}{2\pi \times 6}$$

Multiply 2 and 6 to get 12.

$$\frac{\left(\sqrt{7}+\sqrt{6}\right)\sqrt{6}}{12\pi }$$

Use the distributive property to multiply \sqrt{7}+\sqrt{6} by \sqrt{6}.

$$\frac{\sqrt{7}\sqrt{6}+\left(\sqrt{6}\right)^{2}}{12\pi }$$

To multiply \sqrt{7} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{42}+\left(\sqrt{6}\right)^{2}}{12\pi }$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{42}+6}{12\pi }$$