Finding the square root of 2-digit numbers
ending in 1

Select a 2-digit number and square it.

Drop the last two digits of the square.

Find the largest square root of the remaining digits.
This is first digit of the square root.

The second digit is 1.

Examples:

If the square is 2601:

Drop the last two digits: 26

Find the largest root in 26: 5 × 5 = 25

The first digit is 5. The second digit is 1.

So the square root of 2601 is 51.

See the pattern?

If the square is 8281:

Drop the last two digits: 82

Find the largest root in 82: 9 × 9 = 81

The first digit is 9. The second digit is 1.

So the square root of 2601 is 91.

This process also works for squares of 3-digit numbers
(or more).

For the square 22801, find the largest root of 228:
15x15 = 225. The first two digits are 15, the last
digit is 1, and the square root of 22801 is 151.