Solve sqrt{24}-sqrt{8}*sqrt{1/3}

$$\sqrt { 24 } - \sqrt { 8 } \times \sqrt { \frac { 1 } { 3 } }$$

Evaluate

$$\frac{4\sqrt{6}}{3}\approx 3.265986324$$

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}.

$$2\sqrt{6}-\sqrt{8}\sqrt{\frac{1}{3}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{6}-2\sqrt{2}\sqrt{\frac{1}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$2\sqrt{6}-2\sqrt{2}\times \frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$2\sqrt{6}-2\sqrt{2}\times \frac{1}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2\sqrt{6}-2\sqrt{2}\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

Express 2\times \frac{\sqrt{3}}{3} as a single fraction.

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

Express \frac{2\sqrt{3}}{3}\sqrt{2} as a single fraction.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

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

Combine 2\sqrt{6} and -\frac{2\sqrt{6}}{3} to get \frac{4}{3}\sqrt{6}.

$$\frac{4}{3}\sqrt{6}$$