Solve 2sqrt{3}-2sqrt{12}+sqrt{27}-sqrt{7}

$$2 \sqrt { 3 } - 2 \sqrt { 12 } + \sqrt { 27 } - \sqrt { 7 }$$

Evaluate

$$\sqrt{3}-\sqrt{7}\approx -0.913700503$$

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}.

$$2\sqrt{3}-2\times 2\sqrt{3}+\sqrt{27}-\sqrt{7}$$

Multiply -2 and 2 to get -4.

$$2\sqrt{3}-4\sqrt{3}+\sqrt{27}-\sqrt{7}$$

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

$$-2\sqrt{3}+\sqrt{27}-\sqrt{7}$$

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}.

$$-2\sqrt{3}+3\sqrt{3}-\sqrt{7}$$

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

$$\sqrt{3}-\sqrt{7}$$