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

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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.