Solve -2sqrt{12}+2sqrt{27}

$$-2 \sqrt{ 12 } +2 \sqrt{ 27 }$$

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

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}.

$$-2\times 2\sqrt{3}+2\sqrt{27}$$

Multiply -2 and 2 to get -4.

$$-4\sqrt{3}+2\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Multiply 2 and 3 to get 6.

$$-4\sqrt{3}+6\sqrt{3}$$

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

$$2\sqrt{3}$$