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# This note has been used to help create the Mental Math Tricks wiki

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.

Note by Kartik Kulkarni
2 years, 4 months ago

## Comments

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How about to find cube roots of a number which answer is three-digit number ?? For example 111^3, 267^3, etc · 2 years, 4 months ago

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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 · 2 years, 4 months ago

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So we just do the same ways... Thank you so much.. · 2 years, 4 months ago

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waitwaitwaitwaitwait..whaaaaaaaaaaat? Where did that 3 even come from? The last digit of 1860867 is 7..... · 2 years, 3 months ago

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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. · 2 years, 3 months ago

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So basically the cube of the number you are looking for must have the same last digit as the number in the problem? · 2 years, 3 months ago

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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. · 2 years, 3 months ago

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2, 3, and 7, 8 has at their unit place have their 10's compliments. Rest have the same number as said earlier. · 2 years, 3 months ago

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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! · 2 years, 3 months ago

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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 · 2 years, 3 months ago

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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. · 2 years, 3 months ago

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It works for groups of threes. How adorable. · 2 years, 3 months ago

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ecellent method .its working · 2 years, 3 months ago

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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! · 1 week, 2 days ago

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But it is not useful for non perfect cubes · 1 week, 2 days ago

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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?? · 1 year, 9 months ago

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Very nice & thanks. · 2 years, 1 month ago

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Good Method ....!!! Amazing...!! · 2 years, 2 months ago

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thats just for a sure perfect cube · 2 years, 2 months ago

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Cool....... · 2 years, 3 months ago

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Really very useful trick Thanks:) · 2 years, 3 months ago

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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 · 2 years, 3 months ago

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how to work out cube root of 216216. The answer on face is 66 but that is not the cube root. · 2 years, 3 months ago

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you have to it by long division method · 2 years, 3 months ago

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Very nice and interesting solution · 2 years, 3 months ago

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good one · 2 years, 3 months ago

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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.. · 2 years, 3 months ago

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I would prefer not to use Hindi cause it is confusing me that you have mixed up English & Hindi · 2 years, 3 months ago

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Only works for whole numbers. It's interesting however that you have found this method. How did you come across it? · 2 years, 3 months ago

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excellent method!!! upvoted young mind :) · 2 years, 3 months ago

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I like it · 2 years, 3 months ago

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Who discovered this method? It's really awesome · 2 years, 3 months ago

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i like that method · 2 years, 3 months ago

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Real nice method. I liked it. · 2 years, 3 months ago

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I like this method . · 2 years, 3 months ago

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nice · 2 years, 3 months ago

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you mean x^3 of 226981 , 226971 , 226961 , 226981 , 226881 , all is 61 only by your way. which is incorrect · 2 years, 3 months ago

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you have to know that it it works only for a perfect cube · 2 years, 3 months ago

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I'm sorry I did not understand · 2 years, 3 months ago

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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. · 2 years, 3 months ago

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This method is only applicable for cube numbers that have the cube root with no numbers after the decimal point · 2 years, 3 months ago

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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. · 2 years, 3 months ago

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excellent · 2 years, 3 months ago

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Thank U Very Much.I like Ur Way To solve The Problem. · 2 years, 3 months ago

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Great! Interesting! · 2 years, 3 months ago

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Very helpful. Thank you! · 2 years, 3 months ago

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Really good method... I like it! · 2 years, 3 months ago

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Good solution · 2 years, 3 months ago

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Write a comment or ask a question... Super · 2 years, 3 months ago

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Thanks · 2 years, 3 months ago

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Excellent method · 2 years, 3 months ago

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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. · 2 years, 3 months ago

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In that case we know between which two integers the actual cube root lays. · 2 years, 3 months ago

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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 · 2 years, 3 months ago

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Awesome and unique way to do it!! Thanks!! · 2 years, 3 months ago

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Nice note · 2 years, 3 months ago

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Would largely help me for finding Karl Pearson's coefficient. Thanks. · 2 years, 4 months ago

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Fantastic method Thanks · 2 years, 4 months ago

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Brilliant! Good to learn this from you. Thanks. · 2 years, 4 months ago

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maths is not about approximation and estimation!!!! · 2 years, 4 months ago

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can someone prove it mathematically? · 2 years, 4 months ago

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https://brilliant.org/discussions/thread/long-divison-method-of-cube-root/ · 2 years, 3 months ago

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a + 10 b + 100 c + 1000 d + 10000 e + 100000 f could roughly prove it I guess. · 2 years, 4 months ago

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@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??? · 2 years, 4 months ago

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also 1441's cube root is somewhat 11 And many more numbers after the decimal points · 2 years, 4 months ago

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Well actually,this method is only applicable for actual cube numbers · 2 years, 4 months ago

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Great buddy. Here is the actual method https://brilliant.org/discussions/thread/long-divison-method-of-cube-root/ · 2 years, 3 months ago

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@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) · 2 years, 4 months ago

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well , I didn't think about the estimation part · 2 years, 4 months ago

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cool · 2 years, 4 months ago

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Really cool way...I m looking forward to u to post some cool ways of finding the sum of series.... · 2 years, 4 months ago

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according to this cube root of 125486 should be 56 but actually it is not · 2 years, 2 months ago

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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!! · 2 years, 2 months ago

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OK. what about 125000? · 2 years, 1 month ago

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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) · 2 years, 1 month ago

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216216 · 1 year, 5 months ago

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Comment deleted Apr 05, 2015

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Comment deleted Apr 08, 2015

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Sorry i didnt get u. · 2 years, 1 month ago

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125486 is not a perfect cube and so this method is not applicable for that number · 2 years ago

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knew that already · 2 years, 3 months ago

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do you want to know the exact long division method of finding cube roots though it tedious... :) · 2 years, 3 months ago

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sure. · 2 years, 3 months ago

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https://brilliant.org/discussions/thread/long-divison-method-of-cube-root/ · 2 years, 3 months ago

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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! · 2 years, 3 months ago

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what if we have 7 digited number could u explane me how to do it please · 2 years, 3 months ago

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I just explained it to Jonathan Christianto above · 2 years, 3 months ago

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kk:":":":":":":thanku · 2 years, 3 months ago

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then we have to go by long divison actual method · 2 years, 3 months ago

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