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another way... let 9=a and 80^1/2=b. [looks complex , but on paper, its just 4 steps]

so the eqn is [(a+b)^1/2+(a-b)^1/2]^2. which is of the form [a+b]^2 on expanding, a+b+a-b+2[(a+b)(a-b)]^1/2. we get 2a +2(a^2-b^2)^1/2 put the values back, we get 18+2=20