Which expression is equivalent to √(200)?

Factor out the largest perfect square: $200 = 100\cdot 2$, so $\sqrt{200}=\sqrt{100}\cdot\sqrt{2}=10\sqrt{2}$, choice F. Squaring the answer confirms it: $(10\sqrt2)^2 = 100\cdot 2 = 200$. Choice G, $20\sqrt{2}$, squares to $800$, so it takes out twice the correct root. Choice H, $2\sqrt{10}$, squares to $40$, which comes from factoring $200$ as $4\cdot 10$ and mishandling the pieces. Choice J, $100\sqrt{2}$, pulls the entire $100$ outside the radical without taking its square root. Each wrong choice fails the check of squaring back to 200.