Squaring numbers more than 100

This technique is suitable for finding the square of number that is more than 100.

Example 1:

103 x 103 = 10609



Steps:

Find the difference between 100 and the number. 103 - 100 = 3

1. 103 + 3 = 106(00) <- Add the difference from the number being squared.


2. 3 x 3 = 9 <- Square the difference.


3. 10600 + 9 = 10609.

Example 2:

112 x 112 = 12544

Steps:
Find the difference between 100 and the number. 112 - 100 = 12

1. 112 + 12 = 124(00) <- Add the difference from the number being squared.


2. 12 x 12 = 144 <- Square the difference.


3. 12400 + 144 = 12544.

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Squaring numbers between 51 and 100

This technique is suitable for finding the square of number that falls in range of 51 and 100.

Example 1:

97 x 97 = 9409



Steps:

Find the difference between 100 and the number. 100 - 97 = 3

1. 97 - 3 = 94(00) <- Subtract the difference from the number being squared.

2. 3 x 3 = 9 <- Square the difference.

3. 9400 + 9 = 9409.

Example 2:

76 x 76 = 5776

Steps:

Find the difference between 100 and the number. 100 - 76 = 24

1. 76 - 24 = 52(00) <- Subtract the difference from the number being squared.

2. 24 x 24 = 576 <- Square the difference.

3. 5200 + 576 = 5776.

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Squaring numbers that end in 5

You know that 5 x 5 = 25. However, do you realize that the square of any number that ends with 5, will also contains 25 in the last 2 digits.



Example 1:

25 x 25 = 625

Steps:

Remove the last digit. We get 2.

1 + 2 = 3 <-- Add 1.

3 x 2 = 6 <-- Multiply 2 times the result.

6 and 25 give 625 <-- Concatenate the result with 25.

Example 2:

205 x 205 = 42025

Steps:

Remove the last digit. We get 20.

1 + 20 = 21 <-- Add 1.

21 x 20 = 420 <-- Multiply 20 times the result.

420 and 25 give 42025 <-- Concatenate the result with 25.

Example 3:

315 x 315 = 99225

Steps:

Remove the last digit. We get 31.

1 + 31 = 32 <-- Add 1.

32 x 31 = 992<-- Multiply 31 times the result.

992 and 25 give 99225 <-- Concatenate the result with 25.

If you have better method to share, please don't hesitate to leave your comment.