(sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2 = ?

[sfbay]

(sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2 =

from gmat prep 2

[sfbay]

FYI - it is a perfect squares problem but i was hoping to find a better a better/faster/easier way of doing this.

[MannyRosas]

(sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2=
as a perfect square:
(sqrt(9+sqrt(80))^2 + 2*sqrt(9+sqrt(80))(sqrt(9-sqrt(80)) + sqrt(9-sqrt(80))^2=
9+sqrt(80) + 2*sqrt[(9+sqrt(80))(9-sqrt(80))] + 9-sqrt(80)=
adding the 9s and subtracting the sqrt(80)s:
2*9+2*sqrt[9^2-sqrt(80)^2]=
18+2*sqrt(81-80)=
18+2*1=
20

[RonPurewal]

(sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2=
as a perfect square:
(sqrt(9+sqrt(80))^2 + 2*sqrt(9+sqrt(80))(sqrt(9-sqrt(80)) + sqrt(9-sqrt(80))^2=
9+sqrt(80) + 2*sqrt[(9+sqrt(80))(9-sqrt(80))] + 9-sqrt(80)=
adding the 9s and subtracting the sqrt(80)s:
2*9+2*sqrt[9^2-sqrt(80)^2]=
18+2*sqrt(81-80)=
18+2*1=
20

yep.

[sfbay]

Ron

I know you are not a computer wizard but could those who are add a few buttons on the font ribbon like a sqrt symbol and exp. just tedious to have to put in all those parenthesis and sqrts etc

[RonPurewal]

Ron

I know you are not a computer wizard but could those who are add a few buttons on the font ribbon like a sqrt symbol and exp. just tedious to have to put in all those parenthesis and sqrts etc

yeah, but the cool thing is, now that we have the internet you don't have to worry about that anymore. viz.:
* do a google search for "square root symbol"
* copy
* paste
√ √ √
there you go.