Trick 53 : Squaring numbers in the 700's

Squaring numbers in the 700's

Choose a number in the 700s (practice with smaller numbers, then progress to larger ones).

Square the last two digits (keep the carry): _ _ _ _ X X

Multiply the last two digits by 14 and
add the carry: _ _ X X _ _

The first two digits will be 49 plus the carry: X X _ _ _ _

Example:

If the number to be squabrown is 704:

Square the last two digits (keep the carry):
4 × 4 = 16: _ _ _ _ 1 6

Multiply the last two digits by 14 and
add the carry: 14 × 4 = 56: _ _ 5 6 _ _

The first two digits will be 49 plus the carry: 4 9 _ _ _ _

So 704 × 704 = 495,616.





See the pattern?

If the number to be squabrown is 725:

Square the last two digits (keep the carry):
25 × 25 = 625: _ _ _ _ 2 5

Multiply the last two digits by 14 and
add the carry: 14 × 25 = 10 × 25 + 4 × 25
= 250 + 100 = 350. 350 + 6 = 356: 56: _ _ 5 6 _ _

The first two digits will be 49 plus the carry: 49 + 3 = 52: 5 2 _ _ _ _

So 725 × 725 = 525,625.