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

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

Evaluate

$$\sqrt{6}+5\approx 7.449489743$$

Solution Steps

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

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

The square of \sqrt{6} is 6.

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

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

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

The square of \sqrt{6} is 6.

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

Multiply 5 and 6 to get 30.

$$\frac{6\sqrt{6}+30}{6}$$

Divide each term of 6\sqrt{6}+30 by 6 to get \sqrt{6}+5.

$$\sqrt{6}+5$$

Factor

$$\sqrt{6} + 5 = 7.449489743$$