We have been discussing the method to find the square of two-digit numbers that are greater or less than base numbers. Today we are going to see the square of bigger numbers that are greater than base numbers.
Let us consider 10032
▪The base is taken as 1000.
▪1003 is 3 greater than the base. The increment is 3
▪Add the given number and the increment to get the first part of the answer. 1003+3= 1006.
▪Square the increment to get the second part of the answer. 32 = 9
▪Since the number of digits in the second part should be equal to the number of zeros in the base 9 is taken as 009.
▪Answer: 1006009
Let us try another problem: 100112
▪Here 10000 is the base.
▪11 is the increment.
▪To get the first part of the answer add 11 to the given number.
▪10011 + 11 = 10022
▪Square the increment. 112 = 121.
▪Since we need four digits in the second part write it as 0121.
▪Answer: 100220121
With this method even though the numbers are bigger the calculations are easier and mistakes are minimised.
Do you remember how to square a number that ends in 5? Let me recollect the method.
There are two steps.
Step 1: Multiply part 1 by its consecutive number
Step 2: Square part 2, which is 52
Example: 352
(3 x 4) = 12
52 = 25
Answer: 1225
We can combine the two methods when we do a problem,
Find the square of 10065.
▪Here 10000 is the base.
▪65 is the increment.
▪To get the first part of the answer add 65 to the given number.
10065 + 65 = 10130
▪Square the increment. 652 = (6X7) and 52
10130 4225
Since the number of zeros in the base and the number of digits in the second part of the answer are the same we can directly write it down.
Answer: 101304225
Now you can try: a) 100062, b) 100152, c) 10092, d) 10052, e) 1000752