squares of *5 numbers

If there is a number ending with 5 then it's square can be found easily by the following method. For example lets take the number 135. Then to find its square first replace the ending 5 by 25. Then, multiply the remaining number by its successor.(Here, multiply 13 by its successor, i.e., 14) 135^2=(13 * 14)_25 =182 _ 25=18225

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
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Comments

Nice observation. Do you know why this is true?

Calvin Lin Staff - 6 years, 4 months ago

Means?

Akash Gupta - 6 years, 4 months ago

Sorry, it should have been "why" instead of "what" (edited).

Do you know how to explain the pattern that you observed?

Calvin Lin Staff - 6 years, 4 months ago

@Calvin Lin – Sorry but I cant explain the reason

Akash Gupta - 6 years, 4 months ago

@Calvin Lin – Ya, I have explained it on my blog. Please refer to it. http://www.brainuser1.blogspot.in/2015/09/square-of-5.html

Akash Gupta - 5 years, 7 months ago

@Calvin Lin – I proved it using algebra☺️

Akash Gupta - 3 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$