Solve (sqrt{3}-3sqrt{3}-sqrt{12}+sqrt{27})

$$( \sqrt { 3 } - 3 \sqrt { 3 } - \sqrt { 12 } + \sqrt { 27 } )$$

Evaluate

$$-\sqrt{3}\approx -1.732050808$$

Solution Steps

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

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

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}.

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

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

$$-4\sqrt{3}+\sqrt{27}$$

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}.

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

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

$$-\sqrt{3}$$