Squaring numbers close to the base 10, 100, 1000 and so on (part-2)

Squaring numbers close to base 1000

1025² =?

Notice that 1025 is close to base 1000. So,

1)       Find the surplus or deficit from base 1000.

It is (1025–1000=) 25 surpluses.

2)       Since 1025 is 25 more than base 1000, so add 25 to the entire number, which is 1025+25 = 1050. Write 1050 as the first part of the answer.

3)     Now, since 1000 has 3 zeros so, 3 more digits to go. Find the square of surplus 25 which is 625. Write 625 as the last 3 digits of the answer.

So, our answer is 1,050,625.

Another example, 985² =?

985 is (1000-985=) 15 less than the base 1000.

Subtract 15 from 985, which is 970.

Square of 15 is 225. Write 225 for the last 3 places.

So, our answer is 970225.

Further example, 996² =?

996 is (1000-996=) 4 less than the base 1000.

Subtract 4 from 996, which is 992.

Square of 4 is 16. So, write 016 for the last 3 places. (Notice the extra ‘0’)

So, our answer is 992016.