Squaring Numbers in Range 51-100

Another approach was communicated to me by my late father Moisey Bogomolny.

We are looking to compute A², where A = 50 + a. Instead compute 100·(25 + a) and add a². Example: let A = 57. a = 57 - 50 = 7. 25 + 7 = 32. Append 49 = 7². Answer: 57² = 3249.

Why does this work?

The same algebra as above gives

In general, if the number to be squared is close to a number with a known square, yet another approach is available. Assume we wish to compute 57². Observe that 60² = 3600 and 57 is pretty close to 60. Take the difference: 60 - 57 = 3 and also compute 57 - 3 = 54. Then

	57²	= 60×54 + 3²
		= 3240 + 9
		= 3249.

Why does this work?

It is still the same algebra as above:

A² = (A + x)(A - x) + x².

The whole trick here is to remember some squares, like 6² = 36. The more your remember the better.

|Contact| |Front page| |Contents| |Algebra| |Rapid math| |Store|