what is the square root of 12345678987654321?

Answer 1

111,111,111

Answer 2

False Criticisms: 12,345,678,987,654,321
In her Parade Magazine column of February 25, 2001, Marilyn claims that it is easy to use a Calculator to determine that the square root of 12,345,678,987,654,321 is 111,111,111 (or that 111,111,111 x 111,111,111 is 12,345,678,987,654,321). […]

In order to perform this calculation, a calculator must be able to handle 17 significant digits. Many older calculators can not, although calculators that can are becoming increasingly common.

A calculator handling only nine significant digits will do. 12,345,678,987,654,321 and 111,111,111 have a significance because they were mentioned. Marilyn’s point isn’t that any number with a seventeen digit square can be checked easily on a calculator. Her point was the squared number and square root have obvious patterns. And perhaps, the pattern of the square is related to the squaring of the series of 1’s. This can be easily checked on any calculator.

1 ∙ 1 = 1
11 ∙ 11 = 121
111 ∙ 111 = 12,321
1,111 ∙ 1,111 = 1,234,321
11,111 ∙ 11,111 = 123,454,321

That’s as far as a nine digit calculator can go. Since this establishes the pattern, one can continue safely and painlessly.

111,111 ∙ 111,111 = 12,345,654,321
1,111,111 ∙ 1,111,111 = 1,234,567,654,321
11,111,111 ∙ 11,111,111 = 123,456,787,654,321
111,111,111 ∙ 111,111,111 = 12,345,678,987,654,321

This pattern seemingly stops after 111,111,111.

To check whether your calculator is really capable of handling this task, check its square root of 12,345,678,987,654,320 and 12,345,678,987,654,322, to ensure that the calculator does not report the same square root for values close to 12,345,678,987,654,321.

12,345,678,987,654,321 can be within a 111,111,110 range and the square root still rounds to 111,111,111. The square root of 12,345,678,987,654,322 is 111,111,111.000000005. And the square root of 12,345,678,987,654,320 is 111,111,110.999999995. This scrutiny requires intolerable precision./

Answer 3

I like this one because you can figure it out without a calculator
11*11 = 121
111*111 = 12321
1111*1111 = 1234321
etc...
so by induction, we can presume that the square root of a number of this form with (2n-1) digits is a number with "n" ones.
Your number has 2*9-1 digits, so the square root is
111,111,111 (9 ones)

Answer 4

the square root is:
111.111.111

For those who have the sport to lower the thumb without knowing:

Calculated with Mathematica 4, with 40 digits of precision:

In[1]:= (123456789987654321)^0.5
Out[1] = 111111111
Making the product 111 x 111 by hand are obvious that the 3 last numbers of the result are 321

Answer 5

111^2 = 12321
1111^2 = 1234321
and so on
so 111,111,111^2 = 12345678987654321

Answer 6

At the time of this answer no one has included
-111,111,111
I'm first.

Answer 7

111111111. are its square root

Answer 8

very simple. 111111111 is the correct answer.

Answer 9

Its 111111111

Answer 10

111,111,111
it would b better if u would use a calculator next time u want such answers

Answer 11

15241578829446731184270689971041 is the square root of 12345678987654321.............