Solve frac{2sqrt{6}+5}{2sqrt{6}}

$$\frac { 2 \sqrt { 6 } + 5 } { 2 \sqrt { 6 } }$$

Evaluate

$$\frac{5\sqrt{6}}{12}+1\approx 2.020620726$$

Solution Steps

Rationalize the denominator of \frac{2\sqrt{6}+5}{2\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\left(2\sqrt{6}+5\right)\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\left(2\sqrt{6}+5\right)\sqrt{6}}{2\times 6}$$

Multiply 2 and 6 to get 12.

$$\frac{\left(2\sqrt{6}+5\right)\sqrt{6}}{12}$$

Use the distributive property to multiply 2\sqrt{6}+5 by \sqrt{6}.

$$\frac{2\left(\sqrt{6}\right)^{2}+5\sqrt{6}}{12}$$

The square of \sqrt{6} is 6.

$$\frac{2\times 6+5\sqrt{6}}{12}$$

Multiply 2 and 6 to get 12.

$$\frac{12+5\sqrt{6}}{12}$$