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Comment on Squaring Numbers Ending in 5
Awesome
Great trick! Care to explain
You bet.
You bet.
Notice that a number in the form k5 (where k = the tens digit), can be written as 10k + 5
For example, 35 = 3(10) + 5 and 85 = 8(10) + 5
So, let's take our number, 10k + 5, and square it. We get:
(10k + 5)² = 100k² + 100k + 25
= 100(k² + k) + 25
= 100(k)(k+1) + 25
Notice that, in the above expression, we have the product (k)(k+1).
This represents taking the digit in front of the 5 and multiplying by 1 greater than itself.
Then the "+ 25" part of the expression represents placing "25" after the product of k and 1 greater than k.
Does that make sense?
Interesting, Thanks.
wow didnt knew this technique
dude you are the man
Is this technique applicable
Yes, it applies to all
Yes, it applies to all numbers ending in 5.
For example, to evaluate 205^2, we:
- multiply 20 x 21 to get 420
- add 25 to the end to get 42025
So, 205^2 = 42025
Cheers,
Brent
Awesome trick!
Does this work when there are
For example, how would we mentally square:
115
345
Yes, the technique works for
Yes, the technique works for ANY integer ending with 5.
Take: 115²
11 x 12 = 132
So, 115² = 13225
Take: 345²
34 x 35 = 1190
So, 345² = 119025
Take: 6385²
638 x 639 = 407682
So, 6385² = 40768225
Cheers,
Brent