Speedy finding of Square of numbers near to its base (Part I)

Finding squares is always the interesting thing. The important thing during exams is saving time. Here is the technique to do it.

Case 1: The numbers are less than its base

Square of 97:

Nearest base to 97 to 100. 97 is less than 100 by 3.

Step 1: Subtract 97 by 3 = 94.

Step 2: Square of 3 = 9

Answer: 94 / 09. (Make sure the number of digits is equal to the number of Zeros in the base).

The Answer is 9409. 

Square of 94:

Step 1: 94 – 6 = 88

Step 2: Square of 6 = 36

The Answer is 8836

Square of 995:

Nearest base to 995 is 1000. 995 is less than 1000 by 5.

Step 1: 995 – 5 = 990.

Step 2: Square of 5 = 25.

Answer 990 / 025 (Number of digits must be equal to the number of Zeros in the base)

The Answer is 990025. 

Square of 88

Step 1: 88 – 12 = 76.

Step 2: 12 x 12 = 144

Answer 76 / 144 (Number of digits is more than the number of Zeros in the base. So it must be carry over). It becomes 77 / 44.

The Answer is 7744.