Solve -2sqrt{6}+3sqrt{6}-3sqrt{27}-2sqrt{6}

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

Evaluate

$$-\sqrt{6}-9\sqrt{3}\approx -18.037947011$$

Solution Steps

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

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

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}.

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

Multiply -3 and 3 to get -9.

$$\sqrt{6}-9\sqrt{3}-2\sqrt{6}$$

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

$$-\sqrt{6}-9\sqrt{3}$$