Solve sqrt{108}+sqrt{27}-2sqrt{75}+2sqrt{3}

$$\sqrt { 108 } + \sqrt { 27 } - 2 \sqrt { 75 } + 2 \sqrt { 3 }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$6\sqrt{3}+\sqrt{27}-2\sqrt{75}+2\sqrt{3}$$

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}.

$$6\sqrt{3}+3\sqrt{3}-2\sqrt{75}+2\sqrt{3}$$

Combine 6\sqrt{3} and 3\sqrt{3} to get 9\sqrt{3}.

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

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}.

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

Multiply -2 and 5 to get -10.

$$9\sqrt{3}-10\sqrt{3}+2\sqrt{3}$$

Combine 9\sqrt{3} and -10\sqrt{3} to get -\sqrt{3}.

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

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

$$\sqrt{3}$$