KCC's Quizzes on AQQ256 about square roots in the digital world

N² = 12,345,678,987,654,321; what is N?

11² = 121

So, 110,000,000² = 12,100,000,000,000,000

12² = 144

So, 120,000,000² = 14,400,000,000,000,000

Therefore, the number must be between the two of these.

But the carry between units and 10’s in 11² is interesting because it makes the number a palindrome…

Let’s see if this is a pattern that repeats:

111² = 111 * 111

111² = 111 * 1 + 111 * 10 + 111 * 100 = 111 + 1110 + 111000 = 12321

1111² = 1111 + 11110 + 111100 + 1111000 = 1234321

…

111,111,111² = 12,345,678,987,654,321

N² = 12,345,678,987,654,321; what is N?

11² = 121

So, 110,000,000² = 12,100,000,000,000,000

12² = 144

So, 120,000,000² = 14,400,000,000,000,000

Therefore, the number must be between the two of these.

But the carry between units and 10’s in 11² is interesting because it makes the number a palindrome…

Let’s see if this is a pattern that repeats:

111² = 111 * 111

111² = 111 * 1 + 111 * 10 + 111 * 100 = 111 + 1110 + 111000 = 12321

1111² = 1111 + 11110 + 111100 + 1111000 = 1234321

…

111,111,111² = 12,345,678,987,654,321

Bingo Martin! You get it and with a brilliant development and justifictaion!