Solve sqrt{12}+sqrt{75}+sqrt{108}=

$$\sqrt { 12 } + \sqrt { 75 } + \sqrt { 108 } =$$

Evaluate

$$13\sqrt{3}\approx 22.516660498$$

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}.

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

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}.

$$2\sqrt{3}+5\sqrt{3}+\sqrt{108}$$

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

$$7\sqrt{3}+\sqrt{108}$$

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}.

$$7\sqrt{3}+6\sqrt{3}$$

Combine 7\sqrt{3} and 6\sqrt{3} to get 13\sqrt{3}.

$$13\sqrt{3}$$