# Sneaky Square Roots

Algebra Level 5

Find the largest possible real value of
$$\sqrt{(x-20)(y-x)} + \sqrt{(140-y)(20-x)} + \sqrt{(x-y)(y-140)},$$
subject to $$-40\leq x \leq 100$$ and $$-20\leq y \leq 200$$.

Details and assumptions

Make sure you scroll to the right if necessary. You should see a comma to indicate the end of the expression.

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