Solve sqrt{3}-3sqrt{12}-sqrt{6})*2sqrt{3}+5sqrt{2}=

$$\sqrt { 3 } - 3 \sqrt { 12 } - \sqrt { 6 } ) \times 2 \sqrt { 3 } + 5 \sqrt { 2 } =$$

Evaluate

$$-\sqrt{6}-5\sqrt{3}\approx -11.109743781$$

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}.

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

Multiply -3 and 2 to get -6.

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

Combine \sqrt{3} and -6\sqrt{3} to get -5\sqrt{3}.

$$-5\sqrt{3}-\sqrt{6}$$