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- General GRE Info and Strategies - 7 videos (free)
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- Geometry - 48 videos
- Integer Properties - 34 videos
- Statistics - 28 videos
- Counting - 27 videos
- Probability - 25 videos
- Data Interpretation - 24 videos
- Analytical Writing - 9 videos (free)
- Sentence Equivalence - 39 videos (free)
- Text Completion - 51 videos
- Reading Comprehension - 16 videos

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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

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