Solve (sqrt{24}+2sqrt{1/6})*sqrt{6}=

$$( \sqrt { 24 } + 2 \sqrt { \frac { 1 } { 6 } } ) \times \sqrt { 6 } =$$

Evaluate

$$14$$

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}.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{6} is 6.

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

Cancel out 6, the greatest common factor in 2 and 6.

$$\left(2\sqrt{6}+\frac{\sqrt{6}}{3}\right)\sqrt{6}$$

Combine 2\sqrt{6} and \frac{\sqrt{6}}{3} to get \frac{7}{3}\sqrt{6}.

$$\frac{7}{3}\sqrt{6}\sqrt{6}$$

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

$$\frac{7}{3}\times 6$$

Express \frac{7}{3}\times 6 as a single fraction.

$$\frac{7\times 6}{3}$$

Multiply 7 and 6 to get 42.

$$\frac{42}{3}$$

Divide 42 by 3 to get 14.

$$14$$

Factor

$$2\times 7$$