OA 20

it's kind of long....
to make it wasier get the sq root of 80 and equal it to a variable x
the multiplication will resuly 9+u+2(9+u)^2*(9-u)^2+9-u
multiply the sq roots and solve u i'll get 18+2(81-u^2)^2
u=80^2, so plug that in. i'll cross the sq root, since u is squared: 18+2(81-80)^2
81-80=1 and the sq toor is one. 18+2*1 = 20....
it's a kind of long and boring calculation, but i hope it

using variables here IMO is the best approach.

9 = x, 80 = y

so you have:

{[x+sqrt(y)]^(1/2) + [x-sqrt(y)]^(1/2)}^2

{[x+sqrt(y)]^(1/2) + [x-sqrt(y)]^(1/2)}* {[x+sqrt(y)]^(1/2) + [x-sqrt(y)]^(1/2)}

x + sqrt(y) +{2*[x+sqrt(y)]^(1/2) * [x-sqrt(y)]^(1/2)} +x - sqrt(y)

2{x + [x+sqrt(y)]^(1/2) * [x-sqrt(y)]^(1/2)}

[x+sqrt(y)]^(1/2) * [x-sqrt(y)]^(1/2) is the same thing as sqrt(a)*sqrt(b) = sqrt(a*b)

so you would produce 2*[sqrt(x^2 -y) + x] by simplifying everything.

plug in your numbers now: 2*[sqrt(81-80) + 9]

2*(1+9) = 2*10 = 20

so the answer is E.

hope all that made sense to you.

Also one more thing to notice; it seemed like you approximated your values by taking sqrt(80) ~ 9 which doesn't work b/c notice how the question avoids asking the answer in "approximately" form.

if they ask you the answer in "approximated value", then you can round off, but if the word approximate is deceptively missing, they are asking you for the exact value.

OA is E, all solutions are useful and particularly the shortcut. thanks

OA is E, all solutions are useful and particularly the shortcut. thanks