Solve 2sqrt{12}6sqrt{1/3}-3sqrt{48}

$$2 \sqrt{ 12 } 6 \sqrt{ \frac{ 1 }{ 3 } } -3 \sqrt{ 48 }$$

Evaluate

$$24-12\sqrt{3}\approx 3.215390309$$

Solution Steps

Multiply 2 and 6 to get 12.

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

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}.

$$12\times 2\sqrt{3}\sqrt{\frac{1}{3}}-3\sqrt{48}$$

Multiply 12 and 2 to get 24.

$$24\sqrt{3}\sqrt{\frac{1}{3}}-3\sqrt{48}$$

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

$$24\sqrt{3}\times \frac{\sqrt{1}}{\sqrt{3}}-3\sqrt{48}$$

Calculate the square root of 1 and get 1.

$$24\sqrt{3}\times \frac{1}{\sqrt{3}}-3\sqrt{48}$$

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

$$24\sqrt{3}\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-3\sqrt{48}$$

The square of \sqrt{3} is 3.

$$24\sqrt{3}\times \frac{\sqrt{3}}{3}-3\sqrt{48}$$

Cancel out 3, the greatest common factor in 24 and 3.

$$8\sqrt{3}\sqrt{3}-3\sqrt{48}$$

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}.

$$8\sqrt{3}\sqrt{3}-3\times 4\sqrt{3}$$

Multiply -3 and 4 to get -12.

$$8\sqrt{3}\sqrt{3}-12\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$8\times 3-12\sqrt{3}$$

Multiply 8 and 3 to get 24.

$$24-12\sqrt{3}$$

Factor

$$12 {(2 - \sqrt{3})} = 3.215390309$$