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2\sqrt{2}\times \frac{8\times 2+1}{2}
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}.
2\sqrt{2}\times \frac{16+1}{2}
Multiply 8 and 2 to get 16.
2\sqrt{2}\times \frac{17}{2}
Add 16 and 1 to get 17.
17\sqrt{2}
Cancel out 2 and 2.