Solve frac{sqrt{48}-sqrt{3}}{6}-frac{sqrt{3}}{3}

$$\frac{ \sqrt{ 48 } - \sqrt{ 3 } }{ 6 } - \frac{ \sqrt{ 3 } }{ 3 }$$

Evaluate

$$\frac{\sqrt{3}}{6}\approx 0.288675135$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

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

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

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

Divide 3\sqrt{3} by 6 to get \frac{1}{2}\sqrt{3}.

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

Combine \frac{1}{2}\sqrt{3} and -\frac{\sqrt{3}}{3} to get \frac{1}{6}\sqrt{3}.

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