Solve {l}{sqrt{12}-sqrt{3}}{+sqrt{1/3}}

$$\left. \begin{array} { l } { \sqrt { 12 } - \sqrt { 3 } } \\ { + \sqrt { \frac { 1 } { 3 } } } \end{array} \right.$$

Evaluate

$$\frac{4\sqrt{3}}{3}\approx 2.309401077$$

Solution Steps

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}.

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

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

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{3} is 3.

$$\sqrt{3}+\frac{\sqrt{3}}{3}$$

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

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