Solve -2sqrt{12}-3sqrt{24}-3sqrt{12}

$$- 2 \sqrt { 12 } - 3 \sqrt { 24 } - 3 \sqrt { 12 }$$

Evaluate

$$-6\sqrt{6}-10\sqrt{3}\approx -32.017446532$$

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}.

$$-2\times 2\sqrt{3}-3\sqrt{24}-3\sqrt{12}$$

Multiply -2 and 2 to get -4.

$$-4\sqrt{3}-3\sqrt{24}-3\sqrt{12}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$-4\sqrt{3}-3\times 2\sqrt{6}-3\sqrt{12}$$

Multiply -3 and 2 to get -6.

$$-4\sqrt{3}-6\sqrt{6}-3\sqrt{12}$$

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}.

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

Multiply -3 and 2 to get -6.

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

Combine -4\sqrt{3} and -6\sqrt{3} to get -10\sqrt{3}.

$$-10\sqrt{3}-6\sqrt{6}$$