Solve 2sqrt{3}+sqrt{12}-sqrt{2}7+3sqrt{13}-sqrt{108}

$$2 \sqrt { 3 } + \sqrt { 12 } - \sqrt { 2 } 7 + 3 \sqrt { 13 } - \sqrt { 108 }$$

Evaluate

$$3\sqrt{13}-2\sqrt{3}-7\sqrt{2}\approx -2.546942725$$

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}.

$$2\sqrt{3}+2\sqrt{3}-7\sqrt{2}+3\sqrt{13}-\sqrt{108}$$

Combine 2\sqrt{3} and 2\sqrt{3} to get 4\sqrt{3}.

$$4\sqrt{3}-7\sqrt{2}+3\sqrt{13}-\sqrt{108}$$

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}.

$$4\sqrt{3}-7\sqrt{2}+3\sqrt{13}-6\sqrt{3}$$

Combine 4\sqrt{3} and -6\sqrt{3} to get -2\sqrt{3}.

$$-2\sqrt{3}-7\sqrt{2}+3\sqrt{13}$$