Solve sqrt{3}-2sqrt{27}+6sqrt{12}

$$\sqrt { 3 } - 2 \sqrt { 27 } + 6 \sqrt { 12 }$$

Evaluate

$$7\sqrt{3}\approx 12.124355653$$

Solution Steps

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}.

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

Multiply -2 and 3 to get -6.

$$\sqrt{3}-6\sqrt{3}+6\sqrt{12}$$

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

$$-5\sqrt{3}+6\sqrt{12}$$

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}.

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

Multiply 6 and 2 to get 12.

$$-5\sqrt{3}+12\sqrt{3}$$

Combine -5\sqrt{3} and 12\sqrt{3} to get 7\sqrt{3}.

$$7\sqrt{3}$$