Easy way to find cube roots

Hey guys, I saw a faster way to find cube roots.

We already know some basic cube numbers

$0^{3}$ =0

$1^{3}$ =1

$2^{3}$ =8

$3^{3}$ =27

$4^{3}$ =64

$5^{3}$ =125

$6^{3}$ =216

$7^{3}$ =343

$8^{3}$ =512

$9^{3}$ =729

Now, the common thing here is that each ones digit of the cube numbers is the same number that is getting cubed , except for 2 ,8 ,3 ,7 .

now let us take a cube no like 226981 .

to see which is the cube root of that number , first check the last 3 digits that is 981 . Its last digit is 1 so therefore the last digit of the cube root of 226981 is 1 .

Now for the remaining digits that is 226

Now 226 is the nearer & bigger number compared to the cube of 6 (216)

So the cube root of 226981 is 61

Let us take another example - 148877

Here 7 is in the last digit but the cube of seven's last digit is not seven. But the cube of three has the last digit as 7.

So the last digit of the cube root of 148877 is 3.

Now for the remaining digits 148.

It is the nearer and bigger than the cube of 5 (125).

Therefore the cube root of 148877 is 53.

Let us take another example 54872.

Here the last three digit's (872) last digit is 2 but the cube of 2's last digit is not 2 but the last of the cube of 8 is 2.

So the last digit of the cube root of 54872 is 8.

Now of the remaining numbers (54). It is nearer and bigger to the cube of 3 (27). So therefore the cube root of 54872 is 38.

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}

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

How about to find cube roots of a number which answer is three-digit number ?? For example 111^3, 267^3, etc

Jonathan Christianto - 6 years, 4 months ago

After doing the last three digits , try to find which is the nearest cube number to it for the remaining digits E.g -

$\sqrt[3]{1860867}$

Done with the last three digits and the last digit , & you get 3 as the last digit of $\sqrt[3]{1860867}$

Now find the nearest cube number of1860 & it is 12 (1728)

So therefore $\sqrt[3]{1860867}$ = 123

Kartik Kulkarni - 6 years, 4 months ago

So we just do the same ways... Thank you so much..

Do I have to learn all cubes from 11 to 99 for this method? Isn't there a better method?

Miguel Krasniqi - 1 year, 11 months ago

waitwaitwaitwaitwait..whaaaaaaaaaaat? Where did that 3 even come from? The last digit of 1860867 is 7.....

Patricio Ramos - 6 years, 4 months ago

@Patricio Ramos – Read the note properly , it says 7 is in the last digit but the cube of seven's last digit is not seven. But the cube of three has the last digit as 7.

@Kartik Kulkarni – So basically the cube of the number you are looking for must have the same last digit as the number in the problem?

@Patricio Ramos – No, dude. It occasionally happens, but it ain't no rule. It happens for 1 (1³ = 1), 4 (4³ = 64), 5 (5³ = 125), 6 (6³ = 216), 9 (9³ = 729) and 0 (0³ = 0). But, here we see, it doesn't happen for 2 (2³ = 8), neither 3 (3³ = 27), nor 7 (7³ = 343) and 8 (8³ = 512). I'll always have to check this before find cube roots by this method.

Matheus Abrão Abdala - 6 years, 4 months ago

@Matheus Abrão Abdala – 2, 3, and 7, 8 has at their unit place have their 10's compliments. Rest have the same number as said earlier.

Niranjan Khanderia - 6 years, 4 months ago

Another Interesting fact:: (A) cube of 2= unit digit 8 .....cube of 8=unit digit 2 (B) cube of 3=unit digit 7...... cube of 7= unit digit 3

Bakul Majumder - 6 years, 4 months ago

1, 4, 5, 6, 9 have the unit place of their cubes as the number themselves. But cubes of 2,3 and 8,7 has there unit place as their compliment of 10.

Thank you, a great method to solve the cube roots, so bad it doesn't work with every cubic root, it would save a lot of time in tests. Anyway, thanks!

Guilherme Aleixo - 6 years, 4 months ago

It works for groups of threes. How adorable.

Lovelli Fuad - 6 years, 4 months ago

Write a comment or ask a question...if m=29 and e=13, then m=m+e e=m-e m=m-e then find the new value of m and e??

Eyob Assefa - 5 years, 10 months ago

But it is not useful for non perfect cubes

Raj Bunsha - 4 years, 1 month ago

Really cool way...I m looking forward to u to post some cool ways of finding the sum of series....

sarvesh dubey - 6 years, 4 months ago

cool

vishwathiga jayasankar - 6 years, 4 months ago

@Kartik Kulkarni .... really a nice one ... but i hav a doubt ... take 1331 ..... u get 11 by the method stated above .... if u take 1441 ..... 11 isnt correct ..... in that case .... u cant find whether a no. is a cube no. or not using this method.... rite???

Ganesh Ayyappan - 6 years, 4 months ago

Well actually,this method is only applicable for actual cube numbers

@Kartik Kulkarni ... as soon as i saw ..... i found this interesting and also concluded this is applicable for perfect cubes ... but ur inference of 1441's cube root is around 11 is wrong ..... eg: take 1721 ..... if u infer by the same method as u did above ... it is around 11 ... but actually it can be estimated to 12 ..... (Note: cube root of 1721 = 11.98)

@Ganesh Ayyappan – well , I didn't think about the estimation part

Great buddy. Here is the actual method https://brilliant.org/discussions/thread/long-divison-method-of-cube-root/

Anshul Gupta - 6 years, 3 months ago

also 1441's cube root is somewhat 11 And many more numbers after the decimal points

can someone prove it mathematically?

Anirudh Roy - 6 years, 4 months ago

a + 10 b + 100 c + 1000 d + 10000 e + 100000 f could roughly prove it I guess.

Lu Chee Ket - 6 years, 4 months ago

https://brilliant.org/discussions/thread/long-divison-method-of-cube-root/

maths is not about approximation and estimation!!!!

Sanket Kar - 6 years, 4 months ago

Brilliant! Good to learn this from you. Thanks.

Fantastic method Thanks

Menna Attia - 6 years, 4 months ago

Would largely help me for finding Karl Pearson's coefficient. Thanks.

Jay Mehta - 6 years, 4 months ago

Nice note

Rifath Rahman - 6 years, 4 months ago

Awesome and unique way to do it!! Thanks!!

Yash Kapoor - 6 years, 4 months ago

Just noticed. It actually isn't applicable to numbers other than perfect cubes. For example, if you calculate the cube root of 1,216 using this method, you get 16; actual root is 10.67. They're almost 5.5 numbers apart. If you have any better ways, please post it.

I had answered to a similar question , & this method is only applicable for numbers which have their cube roots with no numbers after the decimal point

In that case we know between which two integers the actual cube root lays.

Excellent method

Diego Armando Pulido Ramos - 6 years, 4 months ago

Thanks

Qgc Gojra - 6 years, 4 months ago

Write a comment or ask a question... Super

Chaitu Kvr - 6 years, 4 months ago

Good solution

Kuttiyam Srinivasan - 6 years, 4 months ago

ecellent method .its working

Raj Miglani - 6 years, 4 months ago

Really good method... I like it!

Mark Bray - 6 years, 4 months ago

Very helpful. Thank you!

Arjun Manoj - 6 years, 4 months ago

Great! Interesting!

Sheikh Waseem - 6 years, 4 months ago

Thank U Very Much.I like Ur Way To solve The Problem.

Narendra Patki - 6 years, 4 months ago

excellent

Venkata Kantipudi - 6 years, 4 months ago

you mean x^3 of 226981 , 226971 , 226961 , 226981 , 226881 , all is 61 only by your way. which is incorrect

ashish jaiswal - 6 years, 4 months ago

I'm sorry I did not understand

By this trick cube root for last 3 digit is depends on unit place digit only? if we consider these numbers which all have 1 as unit place digit , 226981 , 226971 , 226961 , 226221 , 226881 so by the rule cube root should be 61 for all these numbers. which is actually incorrect because numbers are different.

@Ashish Jaiswal – This method is only applicable for cube numbers that have the cube root with no numbers after the decimal point

@Kartik Kulkarni – As I have mentioned in another comment, if the number is not a perfect cube, we at least know the floor and the ceiling of this number.

you have to know that it it works only for a perfect cube

Tarunesh V - 6 years, 4 months ago

nice

Ray Macedo - 6 years, 4 months ago

I like this method .

Real nice method. I liked it.

Nurul Afsar - 6 years, 4 months ago

i like that method

Kibria Robin - 6 years, 4 months ago

Who discovered this method? It's really awesome

Anshul Gupta - 6 years, 4 months ago

I like it

Ashish gupta - 6 years, 4 months ago

excellent method!!! upvoted young mind :)

Rohit Ner - 6 years, 4 months ago

Only works for whole numbers. It's interesting however that you have found this method. How did you come across it?

Gui Lanham - 6 years, 4 months ago

I HAVE SOME CONFUSION THAT WHEN HAM LOG SAME NO. KO LIKHEGE OR KAB NHI........AS 1ST SUM MEN.......226 KA 6 LIKHE AND 981 KA 1 SO ANS. IS 61 BUT 148877 MEN 148 KA 5 KYU LAST NO TO 8 HA SO COMPLEMENTRY IS 2 BUT HERE IS 5..

Mamta Ray - 6 years, 4 months ago

I would prefer not to use Hindi cause it is confusing me that you have mixed up English & Hindi

do you want to know the exact long division method of finding cube roots though it tedious... :)

sure.

Ailene Nunez - 6 years, 4 months ago

good one

Abhijeet Verma - 6 years, 4 months ago

how to work out cube root of 216216. The answer on face is 66 but that is not the cube root.

you have to it by long division method

216216 is not perfect cube ! This method is only for perfect cube

gagandeep kaur - 3 years, 3 months ago

It's really coolest method ever.but can any1 suggests me methods for square root of a decimal number.for eg:square root of 0.56

Rushabh Shah - 6 years, 4 months ago

Really very useful trick Thanks:)

r j - 6 years, 3 months ago

Cool.......

Gaurav Negi - 6 years, 3 months ago

thats just for a sure perfect cube

Angelo Forcadela - 6 years, 3 months ago

Good Method ....!!! Amazing...!!

Mohammad Dilshad - 6 years, 2 months ago

Very nice & thanks.

Narendra Patki - 6 years, 2 months ago

I gave the first person who introduced this to me a very good comment. Features of natural numbers can occasionally been found. Important thing is never let this concept to mislead ourselves when the situation is not whole numbers. I recalled and remember ed again but not really memorized properly. Understand why could make me a better memory perhaps. Hope I can memorize from today onwards!

Lu Chee Ket - 4 years, 1 month ago

But it is not apllicable everywhere..

Abhilash Panda - 3 years, 7 months ago

Data handling

Kumar Sharvan - 3 years, 6 months ago

Cub of 2, 3, 7, 8 we have its compliment of 10.
For 2: it is 10-2=8...........for 8, it is 10-8=2............................ 3, it it 10-3=7, ......for 7, it is 10-7=3

Niranjan Khanderia - 3 years, 1 month ago

What if its a 7digit number?

amara arora - 2 years, 11 months ago

Thank you it is so easy to find cube root of any number thank you very much

Raj Jain - 2 years, 1 month ago

How to find the cube root of 155.3

Amirtha Varshini - 1 year, 10 months ago

what if we have 7 digited number could u explane me how to do it please

Sidharth Batchu - 6 years, 4 months ago

I just explained it to Jonathan Christianto above

kk:":":":":":":thanku

then we have to go by long divison actual method

whats's wrong with these four numbers(2,3,7 and 8)? i mean these are the number which you will never find at the end of any "squared number"( at ones place i mean). and here too the same four number have different digits at ones place. by the way nice trick. thanks!

Dhiraj Upadhyay - 6 years, 4 months ago

Very nice and interesting solution

istmio veneroso - 6 years, 4 months ago

knew that already

Qian Yu Hang - 6 years, 3 months ago

according to this cube root of 125486 should be 56 but actually it is not

devang agrawal - 6 years, 2 months ago

I just found out when this method works,

for eg 125486. last 3 digits = 6, first 3 digist =5,

here 125 is perfect cube , hence it doesnt work.

MY findings = This method only works when neither of the components( 1st 3 digits & last 3 digits) are perfect cube but the number that is comprised of the components is a perfect cube.

In ur case 125486 aint a perfect cube cum 125 which i call a component is.

Hows my Theorem? Thumbs up!!

Mohammed Ali - 6 years, 2 months ago

OK. what about 125000?

Niranjan Khanderia - 6 years, 2 months ago

@Niranjan Khanderia – An adition to my findings: Either both the components aint perfect cube or both are.

125000, fr last 3 digits =0, fr first 3 digits =5

cube root of 125000 is 50.

(Notice that 000 is nothing but 0 and not 1000, 0^3 is 0)

@Mohammed Ali – 216216

Sam Reeve - 5 years, 6 months ago

125486 is not a perfect cube and so this method is not applicable for that number

Kartik Kulkarni - 6 years, 1 month ago

3√79510

Vijay Kotla - 3 years, 4 months ago

I love this mathed

ankit singh - 3 years, 3 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}`	$\boxed{123}$