Solve sqrt{3}+sqrt{12}-sqrt{27}+sqrt{867}

$$\sqrt { 3 } + \sqrt { 12 } - \sqrt { 27 } + \sqrt { 867 }$$

Evaluate

$$17\sqrt{3}\approx 29.444863729$$

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}.

$$\sqrt{3}+2\sqrt{3}-\sqrt{27}+\sqrt{867}$$

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

$$3\sqrt{3}-\sqrt{27}+\sqrt{867}$$

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}.

$$3\sqrt{3}-3\sqrt{3}+\sqrt{867}$$

Combine 3\sqrt{3} and -3\sqrt{3} to get 0.

$$\sqrt{867}$$

Factor 867=17^{2}\times 3. Rewrite the square root of the product \sqrt{17^{2}\times 3} as the product of square roots \sqrt{17^{2}}\sqrt{3}. Take the square root of 17^{2}.

$$17\sqrt{3}$$