Solve (sqrt{24}+sqrt{1/6})*sqrt{6}

$$( \sqrt{ 24 } + \sqrt{ \frac{ 1 }{ 6 } } ) \times \sqrt{ 6 }$$

Evaluate

$$13$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\left(2\sqrt{6}+\sqrt{\frac{1}{6}}\right)\sqrt{6}$$

Rewrite the square root of the division \sqrt{\frac{1}{6}} as the division of square roots \frac{\sqrt{1}}{\sqrt{6}}.

$$\left(2\sqrt{6}+\frac{\sqrt{1}}{\sqrt{6}}\right)\sqrt{6}$$

Calculate the square root of 1 and get 1.

$$\left(2\sqrt{6}+\frac{1}{\sqrt{6}}\right)\sqrt{6}$$

Rationalize the denominator of \frac{1}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

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

Combine 2\sqrt{6} and \frac{\sqrt{6}}{6} to get \frac{13}{6}\sqrt{6}.

$$\frac{13}{6}\sqrt{6}\sqrt{6}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{13}{6}\times 6$$

Cancel out 6 and 6.

$$13$$

Factor

$$13$$