Solve sqrt{48}-sqrt{1/3}+sqrt{12}

$$\sqrt { 48 } - \sqrt { \frac { 1 } { 3 } } + \sqrt { 12 }$$

Evaluate

$$\frac{17\sqrt{3}}{3}\approx 9.814954576$$

Short 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}.

$$4\sqrt{3}-\sqrt{\frac{1}{3}}+\sqrt{12}$$

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

$$4\sqrt{3}-\frac{\sqrt{1}}{\sqrt{3}}+\sqrt{12}$$

Calculate the square root of 1 and get 1.

$$4\sqrt{3}-\frac{1}{\sqrt{3}}+\sqrt{12}$$

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

$$4\sqrt{3}-\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\sqrt{12}$$

The square of \sqrt{3} is 3.

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

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}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 6\sqrt{3} times \frac{3}{3}.

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

Since \frac{3\times 6\sqrt{3}}{3} and \frac{\sqrt{3}}{3} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\times 6\sqrt{3}-\sqrt{3}.

$$\frac{18\sqrt{3}-\sqrt{3}}{3}$$

Do the calculations in 18\sqrt{3}-\sqrt{3}.

$$\frac{17\sqrt{3}}{3}$$