Evaluate
\sqrt{22}+\sqrt{30}+3\sqrt{5}-2\sqrt{2}\approx 14.047418143
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\sqrt{30}+3\sqrt{5}-\sqrt{8}+\sqrt{22}
Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.
\sqrt{30}+3\sqrt{5}-2\sqrt{2}+\sqrt{22}
Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.
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