Solve -3sqrt{12}-2sqrt{27}

$$- 3 \sqrt { 12 } - 2 \sqrt { 27 }$$

Evaluate

$$-12\sqrt{3}\approx -20.784609691$$

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}.

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

Multiply -3 and 2 to get -6.

$$-6\sqrt{3}-2\sqrt{27}$$

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}.

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

Multiply -2 and 3 to get -6.

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

Combine -6\sqrt{3} and -6\sqrt{3} to get -12\sqrt{3}.

$$-12\sqrt{3}$$