Solve sqrt{12}+sqrt{75}-9sqrt{3}+sqrt{27}+sqrt{3}

$$\sqrt { 12 } + \sqrt { 75 } - 9 \sqrt { 3 } + \sqrt { 27 } + \sqrt { 3 }$$

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

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}.

$$2\sqrt{3}+\sqrt{75}-9\sqrt{3}+\sqrt{27}+\sqrt{3}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$2\sqrt{3}+5\sqrt{3}-9\sqrt{3}+\sqrt{27}+\sqrt{3}$$

Combine 2\sqrt{3} and 5\sqrt{3} to get 7\sqrt{3}.

$$7\sqrt{3}-9\sqrt{3}+\sqrt{27}+\sqrt{3}$$

Combine 7\sqrt{3} and -9\sqrt{3} to get -2\sqrt{3}.

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

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}.

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

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

$$\sqrt{3}+\sqrt{3}$$

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

$$2\sqrt{3}$$