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.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

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

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply

Log in to reply

Log in to reply

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.Log in to reply

Log in to reply

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!

Log in to reply

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

Log in to reply

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.

Log in to reply

It works for groups of threes. How adorable.

Log in to reply

Data handling

Log in to reply

But it is not apllicable everywhere..

Log in to reply

Nice method but I have a doubt. Let us take 117 649 as an example. The last digit is 9. Now 117 is nearer to 5^3(125) rather than 4^3(64). So why is the cube root of 117 649, 49 instead of 59. Would really appreciate an answer.

Log in to reply

We should take the number which has highest cube less than 117 in your case but not nearest.

Log in to reply

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!

Log in to reply

But it is not useful for non perfect cubes

Log in to reply

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??

Log in to reply

Very nice & thanks.

Log in to reply

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

Log in to reply

thats just for a sure perfect cube

Log in to reply

Cool.......

Log in to reply

Really very useful trick Thanks:)

Log in to reply

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

Log in to reply

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

Log in to reply

you have to it by long division method

Log in to reply

Very nice and interesting solution

Log in to reply

good one

Log in to reply

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..

Log in to reply

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

Log in to reply

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

Log in to reply

excellent method!!! upvoted young mind :)

Log in to reply

I like it

Log in to reply

Who discovered this method? It's really awesome

Log in to reply

i like that method

Log in to reply

Real nice method. I liked it.

Log in to reply

I like this method .

Log in to reply

nice

Log in to reply

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

Log in to reply

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

Log in to reply

I'm sorry I did not understand

Log in to reply

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.

Log in to reply

Log in to reply

Log in to reply

excellent

Log in to reply

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

Log in to reply

Great! Interesting!

Log in to reply

Very helpful. Thank you!

Log in to reply

Really good method... I like it!

Log in to reply

ecellent method .its working

Log in to reply

Good solution

Log in to reply

Write a comment or ask a question... Super

Log in to reply

Thanks

Log in to reply

Excellent method

Log in to reply

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.

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply

Nice note

Log in to reply

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

Log in to reply

Fantastic method Thanks

Log in to reply

Brilliant! Good to learn this from you. Thanks.

Log in to reply

maths is not about approximation and estimation!!!!

Log in to reply

can someone prove it mathematically?

Log in to reply

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

Log in to reply

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

Log in to reply

@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???

Log in to reply

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

Log in to reply

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

Log in to reply

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

Log in to reply

@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)

Log in to reply

Log in to reply

cool

Log in to reply

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

Log in to reply

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

Log in to reply

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!!

Log in to reply

OK. what about 125000?

Log in to reply

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)

Log in to reply

Log in to reply

Comment deleted Apr 05, 2015

Log in to reply

Comment deleted Apr 08, 2015

Log in to reply

Log in to reply

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

Log in to reply

knew that already

Log in to reply

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

Log in to reply

sure.

Log in to reply

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

Log in to reply

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!

Log in to reply

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

Log in to reply

I just explained it to Jonathan Christianto above

Log in to reply

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

Log in to reply

then we have to go by long divison actual method

Log in to reply