Solve 13sqrt{12}-2sqrt{1/3}+sqrt{48})div2sqrt{3}

$$13 \sqrt { 12 } - 2 \sqrt { \frac { 1 } { 3 } } + \sqrt { 48 } ) \div 2 \sqrt { 3 }$$

Evaluate

$$\frac{88\sqrt{3}}{3}\approx 50.806823689$$

Short 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}.

$$13\times 2\sqrt{3}-2\sqrt{\frac{1}{3}}+\sqrt{48}$$

Multiply 13 and 2 to get 26.

$$26\sqrt{3}-2\sqrt{\frac{1}{3}}+\sqrt{48}$$

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

$$26\sqrt{3}-2\times \frac{\sqrt{1}}{\sqrt{3}}+\sqrt{48}$$

Calculate the square root of 1 and get 1.

$$26\sqrt{3}-2\times \frac{1}{\sqrt{3}}+\sqrt{48}$$

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

$$26\sqrt{3}-2\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\sqrt{48}$$

The square of \sqrt{3} is 3.

$$26\sqrt{3}-2\times \frac{\sqrt{3}}{3}+\sqrt{48}$$

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

$$26\sqrt{3}+\frac{-2\sqrt{3}}{3}+\sqrt{48}$$

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}.

$$26\sqrt{3}+\frac{-2\sqrt{3}}{3}+4\sqrt{3}$$

Combine 26\sqrt{3} and 4\sqrt{3} to get 30\sqrt{3}.

$$30\sqrt{3}+\frac{-2\sqrt{3}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 30\sqrt{3} times \frac{3}{3}.

$$\frac{3\times 30\sqrt{3}}{3}+\frac{-2\sqrt{3}}{3}$$

Since \frac{3\times 30\sqrt{3}}{3} and \frac{-2\sqrt{3}}{3} have the same denominator, add them by adding their numerators.

$$\frac{3\times 30\sqrt{3}-2\sqrt{3}}{3}$$

Do the multiplications in 3\times 30\sqrt{3}-2\sqrt{3}.

$$\frac{90\sqrt{3}-2\sqrt{3}}{3}$$

Do the calculations in 90\sqrt{3}-2\sqrt{3}.

$$\frac{88\sqrt{3}}{3}$$