Solve frac{sqrt{48}}{3}-2/sqrt{12}

$$\frac{ \sqrt{ 48 } }{ 3 } - \frac{ 2 }{ \sqrt{ 12 } }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

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}.

$$\frac{4\sqrt{3}}{3}-\frac{2}{\sqrt{12}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{4\sqrt{3}}{3}-\frac{2}{2\sqrt{3}}$$

Rationalize the denominator of \frac{2}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{4\sqrt{3}}{3}-\frac{2\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{4\sqrt{3}}{3}-\frac{2\sqrt{3}}{2\times 3}$$

Cancel out 2 in both numerator and denominator.

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

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

$$\sqrt{3}$$