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

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

Evaluate

$$12\sqrt{3}-3\sqrt{2}\approx 16.541969004$$

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}.

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

Multiply 2 and 2 to get 4.

$$4\sqrt{3}-6\sqrt{\frac{1}{2}}+2\sqrt{48}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$4\sqrt{3}-6\times \frac{\sqrt{1}}{\sqrt{2}}+2\sqrt{48}$$

Calculate the square root of 1 and get 1.

$$4\sqrt{3}-6\times \frac{1}{\sqrt{2}}+2\sqrt{48}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$4\sqrt{3}-6\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+2\sqrt{48}$$

The square of \sqrt{2} is 2.

$$4\sqrt{3}-6\times \frac{\sqrt{2}}{2}+2\sqrt{48}$$

Cancel out 2, the greatest common factor in 6 and 2.

$$4\sqrt{3}-3\sqrt{2}+2\sqrt{48}$$

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}.

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

Multiply 2 and 4 to get 8.

$$4\sqrt{3}-3\sqrt{2}+8\sqrt{3}$$

Combine 4\sqrt{3} and 8\sqrt{3} to get 12\sqrt{3}.

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

Factor

$$3 {(4 \sqrt{3} - \sqrt{2})} = 16.541969004$$