Shortcut to find the Cube of a number
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.
You may also like:
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I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths
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Recent Comments
Hello I saw the same trick in Vedic Maths India Forum (I think its Copy... – 14Jun13
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January 28th, 2012 - 23:45
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
January 26th, 2012 - 21:05
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.
January 15th, 2012 - 22:31
sir can u find me the cube root of no which not a perfect cube of any no..
January 15th, 2012 - 22:29
sir please tell me how to find the cube root of a no which is not a perfect cube…….
January 4th, 2012 - 08:52
thank for the answer brother, you people did a great job by getting the shortcuts for maths solutions from the vedic maths.
January 4th, 2012 - 08:43
find 52 cube with description. please
January 4th, 2012 - 08:32
i want to find the cube value of 43 with description. please
December 17th, 2011 - 09:44
There are just so many ways to learn math! Appreciate the post.
December 11th, 2011 - 19:27
this is rediculous……is there no shortcut for cube ????
this is more difficult calculating by multiplication is more easy thru vedic maths…
November 24th, 2011 - 14:59
vineet,
is there any other simple method for calculating the cube
please mail me please………..
October 29th, 2011 - 11:40
tell me to find cubes after 20.?
December 25th, 2011 - 19:52
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
October 26th, 2011 - 16:29
Yeahh!! So gud yaar..:-))
September 21st, 2011 - 09:25
can anybody tell me a shortcut way to find cube of three digit number?
July 9th, 2011 - 12:21
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………………….
July 8th, 2011 - 04:35
ara yeear kuch awr bahter do,isa kuch pata hi nahi chal rha hai.
June 30th, 2011 - 20:10
it’s great yaarr….
May 10th, 2011 - 18:13
wonderful!!!!!!!!!
May 10th, 2011 - 18:11
great!!!! learned alot its a wonderful thing that vedic maths is so great
May 3rd, 2011 - 17:08
bouncer gaya saara ka saara…
May 1st, 2011 - 15:23
can improve
April 12th, 2011 - 20:21
wil u pls tell me the short cut method for
a cube root a three digit number
March 29th, 2011 - 07:23
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…
March 29th, 2011 - 14:16
yeah i agreed too
Nilesh
September 28th, 2011 - 20:49
I was trying to tell this method in comment………….found already shared by Biswajit.
March 16th, 2011 - 09:43
i know already this method
June 2nd, 2011 - 00:53
I don’t know pleas can you learn me how i can find cube of a number by shortcut method.
June 2nd, 2011 - 00:56
show the steps or cubing 25
March 16th, 2011 - 09:39
koi khaas method nahi hai.
February 24th, 2011 - 20:39
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.
February 9th, 2011 - 16:29
solid its awesome!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
February 5th, 2011 - 17:36
It is a simple method to understand.
February 5th, 2011 - 14:13
NICE TRICK
January 18th, 2011 - 15:19
how to find cude root of 24,35,47 etc????????????????
October 20th, 2011 - 13:17
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..
January 18th, 2011 - 13:00
how to calucualte 21^3 and 84 ^3
August 28th, 2010 - 13:23
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]
June 13th, 2011 - 21:04
nah, I use this method. very useful for calculating cubes of numbers like, say 76
August 21st, 2010 - 11:41
show the steps or cubing 24
January 5th, 2011 - 11:25
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
then add two rows
8 16 32 64
32 64
——————-
58 102 64 = 13824
August 19th, 2010 - 04:45
hi hate maths
August 19th, 2010 - 04:30
hit me sooooooooooooooooooooooooooooooooooo easy oh yeahh
August 6th, 2010 - 16:16
@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
August 6th, 2010 - 16:00
@ 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
August 22nd, 2011 - 09:02
BUT 64 &48 AIN’T THE 2ND AND THIRD NOS…….
August 6th, 2010 - 15:46
hhh
July 13th, 2010 - 22:48
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…
January 19th, 2011 - 16:02
@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…
May 31st, 2010 - 16:11
dis is SUPERB!!!!!!!!!!!
April 5th, 2010 - 19:41
how to memorize cube of large number say 619…….????…..
or any easy way to find cube of large number like dis…..???…….
April 1st, 2010 - 15:02
how to use this method to get cubes of fractions?…for instance, how to find the cube of 1.06?
February 6th, 2010 - 11:55
Awesome yar.Man na padega.Thanx for this.
January 21st, 2010 - 19:57
if u need detailed explanation for 25^3…pls let me know
August 27th, 2011 - 12:01
plz let me know the methods of 36
January 21st, 2010 - 19:55
Thanks for the appreciation..
25 will be like this
8__20__50__125
__40__100__
__________________
15625
January 21st, 2010 - 17:30
Sorry for giving the square instead of cube.
The cube seems difficult.
January 21st, 2010 - 16:46
* wasy = easy
January 21st, 2010 - 16:46
25 square is wasy.
2*3=6
Hence, 25 square is 625.
November 23rd, 2009 - 17:21
i wanted to see the number 25
plz do it fr me
January 19th, 2011 - 16:04
8 20 50 125
40 100
——————-
1 5 6 2 5
——————–
carry the digits to left each time…
November 17th, 2009 - 23:53
its too gooddddddddddddddd
really nyc shortcut
November 16th, 2009 - 18:54
it was a wonderful shortcut to find a cube of any two digit number …………
thatsz super coolllllllllllllllllllllllllllllllllllllllllllllll!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
December 25th, 2011 - 22:20
plz answrd 28^3