Squaring of Integers in 2 easy steps!

I just figured out this amazing way of squaring numbers with ones digit 5. Suppose you need to find out the square of 35. Then simply square 5 and write down 25 at last and then multiply 3*3 and add 3.That is square the remaining numbers except 5 and add the same value.You will get 12.Since you can also write it as 3 (3) + 3 = 3 (1 + 3) = 3 *4. So,you may just as well multiply the next integer. You can now easily write 35^2 = 1225. In case of another no.,say 125,you take 25 at last and multiply 12 * 13.So,you have 15625. If you are more comfortable in squaring,simply square 12,you'll get 144 and then add 12,you will get 156.So,125^2 = 15625. Rule works for no. whose ones digit is 5. You will probably not find this anywhere else.It was something I came up with while randomly squaring integers.

#NumberTheory

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

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}`	$\boxed{123}$

Comments

Very good that you $\color{#D61F06}{rediscovered}$ this yourself. You may be interested in knowing that square of any two and three digit numbers can be found as under. $(10a\pm b)^2$ write square of a and then of b. (if b is 1, 2 , or 3, write its square as 01, 04 or09) to this $\pm$ 20 times a*b. Say $37^2 = (30+7)^2=\color{#D61F06}{9} \color{#3D99F6}{49} +20*21 = 1369. \\37^2 = (40-3)^2=\color{#D61F06}{16} \color{#3D99F6}{09} -20*12=1369 ~\\ Three ~digit~ number ~the ~same ~way~~\\127^2 =(120+7)^2= \color{#D61F06}{144} \color{#3D99F6}{49} +20*84=16129 \\127^2 = (130-3)^2=\color{#D61F06}{169} \color{#3D99F6}{09} -20*39=16129\\With~5~at~ unit ~place ~it ~is ~ easy.~~~ (10a +5)^2= \color{#D61F06}{a*(a+1)} \color{#3D99F6}{25}.\\125^2=(120 +5)^2= \color{#D61F06}{(12*13)} \color{#3D99F6}{25}= \color{#D61F06}{156} \color{#3D99F6}{25} .$

Niranjan Khanderia - 6 years, 5 months ago

Amazing! Thank you.

Titas Biswas - 6 years, 5 months ago

I have made an addition.

Niranjan Khanderia - 6 years, 5 months ago

@Niranjan Khanderia – Thanks again.Learnt 2 more ways at a go.

Titas Biswas - 6 years, 5 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}`	$\boxed{123}$