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:
- Finding Cube Root – Vedic Maths Way
- Speed Multiplication by 111 : Vedic Maths
- Vedic Multiplication by 11
Who is behind QuickerMaths?
I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths
I believe that if trained properly using powerful tools like Vedic Maths, the immense intellect of human mind can be ignited instantly - find out more
Get Maths Tricks by Email
Recent Comments
Hello I saw the same trick in Vedic Maths India Forum (I think its Copy... – 14Jun13
Horner method can be used to derive shift add multiplication algorithm. Horner's method has lot... – 11Jun13
Horner's method has lot of application. Horner method can be used to derive shift add... – 11Jun13
Howdy! I could have sworn I've been to this website before but after reading through... – 09Jun13
Hi there every one, here every person is sharing these kinds of know-how, so it's... – 09Jun13
Most Popular
- 100% Finding Cube Root – Vedic Maths Way
- 72% You can make a difference
- 62% Shortcut to Find Square of a Number
- 60% Shortcut to find the Cube of a number
- 55% Base Method of Multiplication
- 53% Division in Vedic Mathematics
- 47% Shortcut Method for Multiplication
- 45% Divisibility Rule of 7, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47
- 45% Quicker Maths by M Tyra
- 44% Memory Tricks for Trigonometry
- 42% Current Affairs Books 2013
- 39% Herons Method of Finding Roots
- 38% Simplify Multiplication with the Lattice Method
- 38% Squaring any 2-digit number
- 37% Trick for Adding Time
April 3rd, 2013 - 22:14
sir, i want to know that is there any short method to find the cube of a 3 digit no.? please help…!
April 4th, 2013 - 15:01
Cube of 3 digit numbers
Cube of 3 digit number
One easy method to find the cube of a 3 digit number. let me put an example 462 3
Here let a=4 ; b=6 and c =2
Find the following
ac + b 2 = 8 + 36 = 44 ——(z)
c 3 = 2 3 = 8 ————————————–> 8
3bc 2 = 3X6X4 =72 ——————————> 2 CF =7
3c X (z) = 6 X 44 = 264 + 7=271 —————-> 1 CF =27
b(6ac+b 2 ) = 6(48+36) =504 +27=531 ———-> 1 CF = 53
3a X (z) = 12 X 44 = 528 + 53 =581 ————-> 1 CF =58
3a 2 b = 3 X 16 X 6 = 288 +58= 346 ————-> 6 CF =34
a 3 =64 +34 = 98 ———————————> 8
—————————————————-> 9
so 462 3 = 98611128
April 5th, 2013 - 19:19
Shantani ji,
the term *3 digit number* is too broad.
Lets break it down to *managable* types of 3 digit numbers.
A) The simple cases : eg cube of (105)>>> this can be handled by a process of “mental” calculations .
here the base number is 100 :
In 105 , the excess over the base 100 is 5
Take this 5 and do 3 x 5 =15
The first digit of the answer **FROM THE LEFT** is 1
so that 1 , and attach 15 to it ; you get 115
Next multiply the 15 obtained earlier by the 8excess* 5 ; 15 x 5 = 75
Attach this to 115
So you have 11575
Now take the cube of the excess 5. you get 125 ; attach this also;
11575
125
——————- now addd these
1157625 >>>>>>>is the cube of 105
{ * check the correctness of the answer by the method of dropping
the NINES }
Happy ?
Lets take the cube of (113) :
First digit of the answer from the LEFT is 1
Excess x 3 = 39 ; So 139
Next 39x the excess = 39×13
=(40-1)x 13
= 520 -13
= 507
The cube of 13 = 2197
Place these in this form :
1 3 9
5 0 7
2 1 9 7
——————-Add
Answer >>>>>>>>>>>>>>>> 1 4 4 2 8 9 7
WE MAY CONTINUE, AFTER THERE IS A FEEDBACK FROM YOU
With best wishes.
April 5th, 2013 - 19:25
After pressing *SUBMIT* one finds that the typed formation gets distorted :
Lets see again :
11575
125
—————–on addition
117625
139
507
2197
——————-on adding
1442897
April 5th, 2013 - 19:26
MODERATOR Sahib, can we do something about this distortion after *SUBMIT* is pressed, please
Thank you
March 31st, 2013 - 23:44
nice trick , this trick sufficient only for two digit no, if find to cube for three digit no like 134 0r 115 . wat i hv to do ? if u hv another trick for three digit no. plz explain …thanx
April 1st, 2013 - 10:45
115 cube
first u must know cube of 1 to 20 or 25
Use formula (a+b)³= a³ + 3a²b + 3ab² + b³
(100+15)³=100³+ 3×100²x15+3x100x15² +15³
=1000000+750000+67500+3375
ans= 1820875
April 1st, 2013 - 10:47
sorry for above mistake
115 cube
first u must know cube of 1 to 20 or 25
Use formula (a+b)³= a³ + 3a²b + 3ab² + b³
(100+15)³=100³+ 3×100²x15+3x100x15² +15³
=1000000+450000+67500+3375
ans= 1520875
March 26th, 2013 - 11:16
very nice trick. practice few numbers its so easy.. just one thing is take the correct ratio.. a very useful trick to solve in a less time for competitive exams
March 23rd, 2013 - 14:18
very nice method
March 9th, 2013 - 14:09
Hi..thanks for posting the shortcut. I tried calculating the cube of a number whose tens digit is greater than the units and I got stuck after calculatimg the ratio. for example lets say the number is 31 then the ratio is 3:1 what would be the first line that we write down after 9….?
March 9th, 2013 - 18:33
AABHA ji,
the cube of 31 :
i do it this way>>>>>>> :
working from RIGHT to LEFT ; 1 power 3 = (01)
The 3 (of 31 ) is done 3×3 = (09)
Take this 9 and x it by 3 = (27)
Finally 3 power 3 = (27 )
now arrange them this way : (27) (27)(09)(01)
= 2 7 ( carry 2 , 7) 91
= 29,791
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let’s do this for making the idea sink in :
(41)power 3 , that is 41 cubed ,
41 cubed : 1 rased to 3 = 1
4 x three = 12 { ~ the 1 of this 12 will be carried }
12 x four = 48 { ~this 4 of 48 will be carried over}
4 raised to 3 = 64
Therefore : (64)(carry4 ,
(carry1 , 2)( 1)
=68921
Now are you happy ?
with best wishes
ahmed41
February 25th, 2013 - 16:09
sir i don’t understand plz give some more exmples
February 25th, 2013 - 16:09
sir i don’t understand plz give some exmples
February 21st, 2013 - 16:13
thank you
January 25th, 2013 - 16:32
But it require lots of effort to find out cube of two digit number using this technique when number at ten’s is greater than unit’s….so is there any way to find out more quickly and with less efforts….
December 24th, 2012 - 08:27
Hai please explain how find cube of a given method plz explain breifly i dont understand
September 3rd, 2012 - 19:14
THANK YOU SO MUCH!!!!!!!!
July 10th, 2012 - 11:44
what is the method to find cube of 88,222,6666,…. etc. ?
July 10th, 2012 - 11:42
what is the method to find cube of 222, 88, 6666…etc?
May 24th, 2012 - 17:03
how to find out cube of any number Ex:25,56,86 etc based on your find a cube of any number? i tried your method but i am not getting write answer.
please guide me.
June 11th, 2012 - 18:58
how to find out cube of any number Ex:25,56,86 etc based on your find a cube of any number? i tried your method but i am not getting write answer.
please guide me.
September 6th, 2012 - 12:41
It means that you are making mistakes in calculating. Here is the solution for
25.
Cube of 2, the first letter in the number is 8. Now put the next 3 numbers using the 2:5, that is,
8 20 50 125
40 100
__________ Now start from the left.
8 60 150 125
8+60+(150+12)\5 = 8+60+162\5 = 8+(60+16)\25
8+76\25
(8+7)/625
15625
February 25th, 2013 - 16:16
sir i don’t understand plz give some more exmples tall me about numbers betwen 8&125
April 22nd, 2012 - 13:11
short trick 1-30 cube
April 20th, 2012 - 21:22
For eg:57
5^3=125, 7^3=343
5/7(343)=245
5/7(245)=175 350=175*2,,,,,490=245*2
125 175 245 343
350 490
____________________
185193
May 6th, 2012 - 19:05
will u plz explain the last line ….how it will calculate
April 20th, 2012 - 17:02
one of the best websites for the pupil who attends competitive exams
April 10th, 2012 - 01:14
How to calculate cube of 57, 83???
April 29th, 2012 - 11:47
take ur calculator and find the answer
May 1st, 2012 - 10:08
(57) KA CUBE = 5*5*5 5*5*7 5*7*7 7*7*7
125 175 245 343
350 490
_______________________________________
Now Simply Carry forward & add from R to L =185193
_______________________________________
This is how U can Solve d Cube Of any two digit Number .
June 14th, 2012 - 10:29
Hello!!Mr. vinay, do u call this a shortcut?!
July 2nd, 2012 - 12:44
how u get 350 and 490
July 2nd, 2012 - 12:55
350 and 490 should be under 175 and 245 respectively,,,
August 23rd, 2012 - 21:29
how do u get the 350 and 490 can u explain
March 28th, 2013 - 16:07
57 cube
1) 5 cube= 125
2) 5:7 ratio
5 : 7
125 : ?
(125*7)/5= 175
3) 5 : 7
175 : ?
?=245
4) 5 : 7
245 : ?
? = 343
only do it upto 4 step
now
step1 step2 step3 step4
125 175 245 343
350 490 (Double of step 2 and step 3)
—————————————–
add & carry forward Right To Left
answer 185193
March 14th, 2012 - 19:30
This is a written method of calculating cubes of numbers by paper & pencil.
What is the quick, MENTAL, method ?
March 14th, 2012 - 16:57
Nice way to calculate Cube ..how can we calculate cube of 23.
February 21st, 2013 - 16:42
23^^^ = (20)(23)(26) + (3^^).(23)
The cube of 23 = (520×23 )+ (9×23)
= 11960 +207 = 12167
March 14th, 2012 - 16:52
Ho w to calculate cube of 23 ??
November 20th, 2012 - 15:51
2^3 = 8
In equal proportions:
8 12 18 27
24 36
4 5 2
———————-
12 1 6 7
= 12167
March 3rd, 2012 - 15:59
This ” Vedic” method is OK if one has to *calculate* the cubes of numbers in writing.
Do you have a method of getting these answers, totally by mental calculation, from inside ones head ??
February 15th, 2012 - 15:42
very nice and quicker way to do mathematics