Lesson: Squaring Numbers Ending in 5

Comment on Squaring Numbers Ending in 5

Awesome

Great trick! Care to explain HOW (or WHY) it works?
greenlight-admin's picture

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 before. thanks for sharing :)

dude you are the man

Is this technique applicable for a 3digit number too?
greenlight-admin's picture

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 more than 2 digits being squared (where the tens digit isn't zero)?

For example, how would we mentally square:

115
345
greenlight-admin's picture

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

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