lovely

answer is 1 :)

u'll observe a series

c
11 root .....after deciaml u hav 3166

1111 root ....after decimal u hav 33166

similarly ............for diffrnce of 2

i mean so nw 1998 is d 1998 term

so it will hav 1998/2...... 3's......ie 999 3's

so after 3 u hav 1 .........
so answer is 1

cheero~

nishu bhayh i wan a golden or else mein mani ka tarika apnaungi ;)

wat was/is mani ka tarika

@ mrunal , i cant get ur method.........

here is my method(a bit bookish) but i cant get anything else..[2][2]

1000th digit after decimal pt. of √N will be unit digit of 10¹⁰⁰⁰√N
=>1000¹⁰⁰⁰(√10¹⁹⁹⁸-1)/3
=>√10³⁹⁹⁸-10²⁰⁰⁰/3

using the fact that,
(10¹⁹⁹⁹-7)²<10³⁹⁹⁸-10²⁰⁰⁰<(10¹⁹⁹⁹-4)²
=>(10¹⁹⁹⁹-7)/3<10¹⁰⁰⁰√N<(10¹⁹⁹⁹-4)/3
=>33...........31<10¹⁰⁰⁰√N<33..........32

=> answer will be 1

any better method is welcome.....i am eagerly waiting for it....

c
11 root .....after deciaml u hav 3166

1111 root ....after decimal u hav 33166

similarly ............for diffrnce of 2

arey means dekh
jab 2 1's hai so u get 31667 aise kuch after decimal

jab 4 1's hai so u get 33167........

jab 6 1's hai u get 33367

u observe that jitne 1's hai use aadha 3 hai decimal ke baad

so jab 1998 1's hai u hav 999 3's n afetr 3 u hav 1 so 1000th is 1