Finding the square root of perfect squares
ending in 5

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 5.

Examples:

If the square is 9025:

Drop the last two digits: 90

Find the largest root in 90: 9 × 9 = 81

The first digit is 9. The second digit is 5.

So the square root of 9025 is 95.

See the pattern?

If the square is 4225:

Drop the last two digits: 42

Find the largest root in 42: 6 × 6 = 36

The first digit is 6. The second digit is 5.

So the square root of 4225 is 65.

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

For the square 15625, find the largest root of 156:
12x12 = 144 (not 13x13 = 169). The first two digits are 12, the last
digit is 5, and the square root of 15625 is 125.