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\sqrt{2}\sqrt{16}\sqrt{2}\sqrt{6}
Factor 32=2\times 16. Rewrite the square root of the product \sqrt{2\times 16} as the product of square roots \sqrt{2}\sqrt{16}.
2\sqrt{16}\sqrt{6}
Multiply \sqrt{2} and \sqrt{2} to get 2.
2\times 4\sqrt{6}
Calculate the square root of 16 and get 4.
8\sqrt{6}
Multiply 2 and 4 to get 8.