Evaluate
\sqrt{3}\left(\sqrt{6}+4\right)\approx 11.170843917
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1\left(2\sqrt{2}+\sqrt{3}\right)\sqrt{6}
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}.
\left(2\sqrt{2}+\sqrt{3}\right)\sqrt{6}
Use the distributive property to multiply 1 by 2\sqrt{2}+\sqrt{3}.
2\sqrt{2}\sqrt{6}+\sqrt{3}\sqrt{6}
Use the distributive property to multiply 2\sqrt{2}+\sqrt{3} by \sqrt{6}.
2\sqrt{2}\sqrt{2}\sqrt{3}+\sqrt{3}\sqrt{6}
Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.
2\times 2\sqrt{3}+\sqrt{3}\sqrt{6}
Multiply \sqrt{2} and \sqrt{2} to get 2.
4\sqrt{3}+\sqrt{3}\sqrt{6}
Multiply 2 and 2 to get 4.
4\sqrt{3}+\sqrt{3}\sqrt{3}\sqrt{2}
Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.
4\sqrt{3}+3\sqrt{2}
Multiply \sqrt{3} and \sqrt{3} to get 3.
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