Quicker Maths

Shortcut to find the Cube of a number

Posted on October 30, 2009

Very often we have to find the cube, i.e. third power of 2 digit numbers. Cubes of very large numbers are rarely used.

Cubes of all the single digits should be memorized. Find below the table of cubes of first ten natural numbers -

13 = 1,              23 = 8,              33 = 27,            43 = 64,            53 = 125,

63 = 216,          73 = 343,          83 = 512,          93 = 729,          103 = 1000

To find the cube of any 2 digit number, we have to take the following steps

First Step: The first thing we have to do is to put down the cube of the tens-digit in a row of 4 figures. The other three numbers in the row of answer should be written in a geometrical ratio in the exact proportion which is there between the digits of the given number.

Second Step: The second step is to put down, under the second and third numbers, just two times of second and third number. Then add up the two rows.

Finding the cube of 12

Or, 123 = ?

First Step: Digit in ten’s place is 1, so we write the cube of 1. And also as the ratio between 1 and 2 is 1:2, the next digits will be double the previous one. So, the first row is

1 2 4 8

Step II: In the above row our 2nd and 3rd digits (from right) are 4 and 2 respectively. So, we write down 8 and 4 below 4 and 2 respectively. Then add up the two rows.

Ex 2: 163 = ?

Soln:

Explanations: 13 (from 16) = 1. So, 1 is our first digit in the first row. Digits of 16 are in the ratio 1:6, hence our other digits should be 1×6 = 6, 6×6 = 36, 36×6 = 216. In the second row, double the 2nd and 3rd number is written. In the third row, we have to write down only one digit below each column (except under the last column which may have more than one digit). So, after putting down the unit-digit, we carry over the rest to add up with the left-hand column. Here,

i) Write down 6 of 216 and carry over 21.

ii) 36 + 72 + 21 (carried) = 129, write down 9 and carry over 12.

iii) 6 + 12 + 12 (carried) = 30, write down 0 and carry over 3.

iv) 1 + 3 (carried) = 4, write down 4.

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Posted by Vineet Patawari

1. I have a question

A number raise to 2 e.g (4)2 is called square of a number. A number raise to 3 e.g (4)3 is called cube of a number. Likewise what is (10.25)120 called. And is there any simple way to calculate it manually other than the same old method of multiplying 10.25 120 times

2. Kindly give any shortcut to find out the cube root of a given fraction no such that 0.000000343. The main problem is to maintain the zeroes in the solution after point.

3. sir can u find me the cube root of no which not a perfect cube of any no..

4. sir please tell me how to find the cube root of a no which is not a perfect cube…….

5. thank for the answer brother, you people did a great job by getting the shortcuts for maths solutions from the vedic maths.

6. find 52 cube with description. please

7. i want to find the cube value of 43 with description. please

8. There are just so many ways to learn math! Appreciate the post.

9. this is rediculous……is there no shortcut for cube ????
this is more difficult calculating by multiplication is more easy thru vedic maths…

10. vineet,
is there any other simple method for calculating the cube

11. tell me to find cubes after 20.?

• dekho sirisha aap 24 le lo
isko 4 part me divide karo
—- —– —– —–
ab aap tens digit mtlb 2 ka cube karo 2*2*2=8 or ise first blank pe fill karo
8 —— —— ——–
ab 24 ka ratio karo 2:4 or isemultiply karo 8 se

4/2*8=16
ab dusri blank me fill karo
8 16 —— ——–
ab 4/2*16=32
ab tisri blank me fill karo

8 16 32 ——–
isi tra4/2*32=64

8 16 32 64
ab 2nd or 3rd ko double kardo
8 16 32 64
32 64
———————————————-
4
———————————————
aap k ans ka last digi hai 4 or jo 6 hai use carry karo
6
8 16 32 64
32 64
———————————————-
102 4
———————————————
ab 10 ko carry karo
10
8 16 32 64
32 64
———————————————-
58 2 4
ab 5 ko carry karo
5
8 16 32 64
32 64
———————————————-
8 0 4
———————————————
5
8 16 32 64
32 64
———————————————-
13 8 0 4 that is your ans aaap try karo baohat easy hai

12. Yeahh!! So gud yaar..:-))

13. can anybody tell me a shortcut way to find cube of three digit number?

14. sir,plz simpel way step by step find the even and odd number cub methord send my e-mail id (mritunjay.gkp123@gmail.com).plz help me sir.Now send………………….

15. ara yeear kuch awr bahter do,isa kuch pata hi nahi chal rha hai.

16. it’s great yaarr….

17. wonderful!!!!!!!!!

18. great!!!! learned alot its a wonderful thing that vedic maths is so great

19. bouncer gaya saara ka saara…

20. can improve

21. wil u pls tell me the short cut method for
a cube root a three digit number

22. actually this method is nothing but..
using
(a+b)3 = a3 + a2b + ab2 + b3
+2a2b+2ab2
————————————
= a3 + 3a2b + 3ab2 + b3
simple…

ie.. cube of 23 is

2 x2x2 2x2x3 2x3x3 3x3x3
2×12 2×18
—————————————————–

= and then solve this
no need to take ratio… ))

23. i know already this method

24. koi khaas method nahi hai.

25. good one but i am little week in maths so it takes time to understand so can u explain cube in a more simple way…i will b really greatful…….thanks a lot.

26. solid its awesome!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

27. It is a simple method to understand.

28. NICE TRICK

29. how to find cude root of 24,35,47 etc????????????????

• if u want to find the cube of your given no. then u can apply (a+b)^3 method but u have to know firstly simple cube value of no. within 10 and your multiplication should fast ok..

30. how to calucualte 21^3 and 84 ^3

31. simple straight multiplication is SOOOOOOOOOOOOOOO much easier.
Say 19cube

19×19=361
361×19=6859 [solving this is quicker and easier than the above so called quick method]

• nah, I use this method. very useful for calculating cubes of numbers like, say 76

32. show the steps or cubing 24

• ratio of no is 4/2
ist row is 2^3 2^3*2 2^3*2*2 2^3*2*2*2
2nd row dpuble of 2nd and 3rd digit from d right
32 and 64

8 16 32 64
32 64
——————-
58 102 64 = 13824

33. hi hate maths

34. hit me sooooooooooooooooooooooooooooooooooo easy oh yeahh

35. @nitz
for 619 type 3 digit number

let the ratio be 6:19 so multiplying factor will be 19/6

now

so in 1st line the numbers will be 6^3 6^3*19/6 6^3*19/6*19/6 6^3*19/6*19/6*19/6
ie. 216 684 2166 6859
………..1368 4332
_____________________
(now take 2 -2 digits down nd rest 2 digits as carryover in the addition ie)
21 65 68
ie. 216 684 2166 6859
………..1368 4332
_______________________
237 17 66 59

36. @ kushagra
for 43^3
ratio is 3/4..so 1st no =64; next 64*3/4, next 64*3/4*3/4 nd last 64*3/4*/4*3/4
rest procedure same as before..

64 48 36 27
96 72
____________
79 5 0 7

• BUT 64 &48 AIN’T THE 2ND AND THIRD NOS…….

37. sir the idea is brilliant… but i faced confusion when i was trying it 43^3… cud u tell me how to do it fr such numbers…

• @kushagra:

i know u wil b confused while writing the ratios beside the original num…
first divide the number by 4 here and multiply by unit digit number 3 here.. it wil b much easier.. u can save ink in this way…

38. dis is SUPERB!!!!!!!!!!!

39. how to memorize cube of large number say 619…….????…..
or any easy way to find cube of large number like dis…..???…….

40. how to use this method to get cubes of fractions?…for instance, how to find the cube of 1.06?

41. Awesome yar.Man na padega.Thanx for this.

42. if u need detailed explanation for 25^3…pls let me know

43. Thanks for the appreciation..

25 will be like this

8__20__50__125
__40__100__

__________________
15625

44. Sorry for giving the square instead of cube.

The cube seems difficult.

45. * wasy = easy

46. 25 square is wasy.

2*3=6

Hence, 25 square is 625.

47. i wanted to see the number 25

plz do it fr me

48. its too gooddddddddddddddd
really nyc shortcut

49. it was a wonderful shortcut to find a cube of any two digit number …………

thatsz super coolllllllllllllllllllllllllllllllllllllllllllllll!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii