Tutorial 57 |
Squaring numbers in the 700's
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- 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 _ _ _ _
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Example:
- If the number to be squared 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 squared 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.
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