how to determine number of digits in squared value

[defeated_soldier]

confusion:

squaring of any number gives how many digits ? how do i know ? any formula , tips/tricks ?

say 1234^2 = how many digits it will give ?


(1111)^2 = how many digits ?

 

[tkhunny]

0^2 = 0
9^2 = 81

Looks like squaring 1 leads to 1 or 2

10^2 = 100
99^2 = 9801

Looks like squaring 2 leads to 3 or 4

 

[defeated_soldier]

i want to predict the number of digits of the followings

(1)^2=1
(11)^2=121
(111)^2=12321
(1111)^2=1234321

do you see any pattern ?

 

[Denis]

1,3,5,7...
So 11111^2 = 9 digits

 

[defeated_soldier]

i meant whether its called pascals triangle or some mathematical pattern ?

 

[TchrWill]

squaring of any number gives how many digits ? how do i know ? any formula , tips/tricks ?

Jot down the number 316227766.....as far out as you wish.

The sequence of numbers given derive from the square root os any odd number of consecutive 9's.

The number of digits in n^2 is given by

..n......................Digits in n^2
10^0 - 3................1
4 - 9.....................2
10^1 - 31.............3
32 - 99.................4
10^2 - 316...........5
317 - 999..............6
10^3 - 3162..........7
3163 - 9999..........8
10^4 - 31622........9
31623 -- 99999....10

and so on.