Evaluate
20\sqrt{22}\approx 93.808315196
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2\sqrt{11}\left(3\sqrt{2}-5\sqrt{2}+3\sqrt{32}\right)
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{11}\left(-2\sqrt{2}+3\sqrt{32}\right)
Combine 3\sqrt{2} and -5\sqrt{2} to get -2\sqrt{2}.
2\sqrt{11}\left(-2\sqrt{2}+3\times 4\sqrt{2}\right)
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{11}\left(-2\sqrt{2}+12\sqrt{2}\right)
Multiply 3 and 4 to get 12.
2\sqrt{11}\times 10\sqrt{2}
Combine -2\sqrt{2} and 12\sqrt{2} to get 10\sqrt{2}.
20\sqrt{11}\sqrt{2}
Multiply 2 and 10 to get 20.
20\sqrt{22}
To multiply \sqrt{11} and \sqrt{2}, multiply the numbers under the square root.
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