Solve sqrt{24}-18sqrt{1/6}

$$\sqrt { 24 } - 18 \sqrt { \frac { 1 } { 6 } }$$

Evaluate

$$-\sqrt{6}\approx -2.449489743$$

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}.

$$2\sqrt{6}-18\sqrt{\frac{1}{6}}$$

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

$$2\sqrt{6}-18\times \frac{\sqrt{1}}{\sqrt{6}}$$

Calculate the square root of 1 and get 1.

$$2\sqrt{6}-18\times \frac{1}{\sqrt{6}}$$

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

$$2\sqrt{6}-18\times \frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$2\sqrt{6}-18\times \frac{\sqrt{6}}{6}$$

Cancel out 6, the greatest common factor in 18 and 6.

$$2\sqrt{6}-3\sqrt{6}$$

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

$$-\sqrt{6}$$