INSTANT SQUARES
25 x 25 = 625. 75 x 75 = 5625... A5 x A5 is (A)(A+1)25. Why does this work?
Well, from your knowledge of place value, you know that any number A5 can be written as 10A + 5. For example 25 = 10 x 2 + 5 and 75 = 10 x 7+5.
So what happens when we square such a number?
A5 x A5 = (10A + 5)(10A+5) = 100A.A + 100A + 25
= 100A (A+1) + 25
= 100 . A(A+1) + 25
We know that the 100 is simply converting the digit to its proper place value. A is a digit, so is A+1. The value of (A+1) is 100(A+1)
