Solve sqrt{33}-sqrt{12}+sqrt{27}

$$\sqrt { 33 } - \sqrt { 12 } + \sqrt { 27 }$$

Evaluate

$$\sqrt{3}+\sqrt{33}\approx 7.476613454$$

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}.

$$\sqrt{33}-2\sqrt{3}+\sqrt{27}$$

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}.

$$\sqrt{33}-2\sqrt{3}+3\sqrt{3}$$

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

$$\sqrt{33}+\sqrt{3}$$