A nice square root problem | Learn Math Olympiad question solution

Learn the easy method to solve square root related problems. This video tells step wise how to solve a tricky square root question. If you like the video, please like & subscribe the channel.

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[stefanocspt]

Short: x=1998 => 4x=7992 => sqrt(1998^2+7992+4) => sqrt(x^2+4x+4) = sqrt((x+2)^2)=x+2 => 1998+2 = 2000

[Birol]

My solution way ist:
1998=a
7996=4a+4, so the equation ist:
a²+4a+4 = (a+2)²
√(a+2)²= a+2
=1998+2
=2000 is the answer.

[petersmith]

Very nice. I missed the obvious that 7996 = 4 x 1999. But, starting with 1998 = 2000-2 gets you there just as quickly.

[devondevon]

2, 000
let n = 2, 000, then
1998 = n-2
1998^2 = (n-2)^2 = n^2 + 4 -4n
7996 = 8, 000- 4
7996 = 4n-4
sqrt (1998^2 + 7996) =
sqrt (n^2 + 4-4n + 4n-4)
sqrt (n^2)
n = 2000 Answer