Evaluate
\sqrt{2}+2\sqrt{3}+3\approx 7.878315178
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2\sqrt{3}-4\sqrt{2}+\sqrt{50}+\sqrt{9}
Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.
2\sqrt{3}-4\sqrt{2}+5\sqrt{2}+\sqrt{9}
Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.
2\sqrt{3}+\sqrt{2}+\sqrt{9}
Combine -4\sqrt{2} and 5\sqrt{2} to get \sqrt{2}.
2\sqrt{3}+\sqrt{2}+3
Calculate the square root of 9 and get 3.
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