# 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 -**

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, 10^{3} = 1000

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**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, 12^{3} = ?

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 2^{nd} and 3^{rd} 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: 16^{3} = ?

Soln:

Explanations: 1^{3 }(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 2^{nd} and 3^{rd} 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.

Plese tell the method to find::

The least number to be added with 1720 to make it as a perfect cube??

TO FIND THE SQUARE OF A NO. WHOSE UNIT PLACE IS 5

EG:-if wehave 2 find the square of 15 then multiply first 5*5 then multiply 1 with

more than 1 i.e 1*2=2 & wite 2 before 25 i.e 225

THANK YOU SO MUCH!!!!!!!!

what is the method to find cube of 88,222,6666,…. etc. ?

what is the method to find cube of 222, 88, 6666…etc?

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.

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.

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

STEP 1. TAKE ANY NUMBER U WANT TO FIND THE CUBE.

STEP 2. WRITE THE CUBE OF THE DIGIT PLACE NUMBER..

for eg: if 56 is the number… write the cube of 6.. ie 216

STEP 3. WHATEVER ANS U GET WRITE ITS LAST DIGIT N CARRY THE REMNG NUMBERS..

for eg: in above eg write 6 and carry 21

STEP 4. THEN MULTIPLY BOTH THE DIGITS OF THE NUMBER U SELECTED TO FIND THE CUBE.AND AGAIN MULTIPLY THAT ANS BY 3.

for eg: if u select 56… then multiply 5 and 6 ie 30 and multiply 30 by 3.. ie 90

STEP 5: MULTIPLY THE ANS U GOT BY THE NUMBER U SELECTED TO FIND THE CUBE…

for eg: ie in above eg multiply 90 by 56 ie = 5040

STEP 6. NOW, CONSIDER ONLY THE LAST TWO DIGITS AND CARRY THE REMAINING OF THE ANS U GOT AND ADD THE LAST TWO DIGITS BY CARRY NUMBER IN STEP 3

for eg: the carry number was 21 and the last two digit of ans is 40.. so add 40 and 21 ie=61

STEP 7. NOW WRITE THAT NO. ON THE LEFT OF ANS U GOT IN STEP 2.

for eg… cube of 6 216… u wrote 6 and carried 21.. by following step 5 and 6.. u got 41,,, so write it as … 416

STEP 8: NOW FIND THE CUBE OF REMAINING DIGITS OF THE NUMBER U SELECTED AND ADD IT BY THE CARRY IN STEP 6.. AND WRITE THE ANS BESIDE STEP 7

for eg: cube of number 5 in 56 is 125… add it by 50 (carry in step 6).. ie 125+50=175.. now write 175 beside 416… ie 175416

STEP 9: THE CUBE OF UR NUMBER IS READY

TRY IT IT IS MY INVENTION

JUGAL

short trick 1-30 cube

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

will u plz explain the last line ….how it will calculate

one of the best websites for the pupil who attends competitive exams

How to calculate cube of 57, 83???

take ur calculator and find the answer

(57) KA CUBE = 5*5*5 5*5*7 5*7*7 7*7*7

125 175 245 343

350 490

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Now Simply Carry forward & add from R to L =185193

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This is how U can Solve d Cube Of any two digit Number .

Hello!!Mr. vinay, do u call this a shortcut?!

how u get 350 and 490

350 and 490 should be under 175 and 245 respectively,,,

how do u get the 350 and 490 can u explain

This is a written method of calculating cubes of numbers by paper & pencil.

What is the quick, MENTAL, method ?

Nice way to calculate Cube ..how can we calculate cube of 23.

Ho w to calculate cube of 23 ??

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 ??

very nice and quicker way to do mathematics