Solve 2sqrt{3}-3sqrt{12}+2sqrt{18}

$$2 \sqrt{ 3 } -3 \sqrt{ 12 } +2 \sqrt{ 18 }$$

Evaluate

$$2\sqrt{3}\left(\sqrt{6}-2\right)\approx 1.557078144$$

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}.

$$2\sqrt{3}-3\times 2\sqrt{3}+2\sqrt{18}$$

Multiply -3 and 2 to get -6.

$$2\sqrt{3}-6\sqrt{3}+2\sqrt{18}$$

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

$$-4\sqrt{3}+2\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

Multiply 2 and 3 to get 6.

$$-4\sqrt{3}+6\sqrt{2}$$