Shortcut Methods for finding the Cube of a number | number cube tricks

  Easy methods for Cube of a Number | cube of a number calculator

Cube of a number means , If any number is multiplied by itself three times, then the product is called the cube of that number.

Generally the cube of a number denoted as, 3 is written a little up to the right of the numbers.

Here Discussed different easy methods to find the cube of a number without calculator. It will help to all students to do fast calculation in there regular and commutative exams.

First remember cube of a number from 1 to 10. 

( 1³= 1 ;

2³= 8 ;

3³= 27 ;

4³= 64 ;

5³= 125 ;

6³= 216 ;

7³= 343 ;

8³= 512 ;

9³= 729 ;

10³= 1000 )

As per the given number we can choose the method for cube of that number

Method : 1 (Cube of a Number End with Zero )

Ex. 1 : Find the cube of  70 ( 70³= ? )

Simple we can write the value of  7³  and add three zeros in right side. i.e 7³  = 343  and  70³ = 343000

Method : 2 ( Cube of a number just near to ten place)

Ex. 1 : Find the cube of 11 ( 11³= ? )

Use the simple algebra formula  (a + b)³ = a³ + 3a²b + 3ab² + b³. 

we can write 11³  = ( 10 + 1 )³ . So here take a = 10 , b = 1 then

( 10 + 1 )³ = 1000 + 300 + 30 + 1 = 1331.

Ex. 2 : Find the cube of 48 ( 48³= ? )

Use the simple algebra formula  (a – b)³ = a³ – 3a²b + 3ab² – b³. 

we can write 48³  = (50- 2 )³ . So here take a = 50 , b = 2 then

( 50 – 2 )³ = 125000 – 15000 + 600 – 8 = 110592.

Method : 3 (Cube of  two digit number).

Ex. 1 : Find the cube of  68 ( 68³= ? )

Take formula (a + b)³ = a³ + 3a²b + 3ab² + b³.  and here assume  Here, a = 6 and b =8.

Step 1 : Take b³ = 8 x 8 x 8 = 512. Take lost digit into the answer last place and remaining value to be add to next step.

i.e Ans :  _ _ _ _ _ 2  and 51 to be add in the next step.

Step 2 : Take 3ab² = 3  x 6 x 64 =  3 x 384 = 1152 and 51 ( from previous step). So 1152 + 51 = 1203. Here Take lost digit into the answer next place and remaining value to be add to next step.

i.e Ans :  _ _ _ _ 3 2  and 120 is to be add in the next step.

Step 3 : Take 3a²b =(3  x 36 x 8) + 120=  864 + 120 = 984.  Here Take lost digit into the answer next place and remaining value to be add to next step.

i.e Ans :  _ _ _43 2  and  98 is to be add in the next step.

Step 4 : Take a² =(6 x 6 x 6) + 98=  216 + 98 = 314.  Take this  value into the answer next places.

i.e  Ans : 31443 2.

 

Therefore, (68)³ = 314432.

Method : 4 ( Cube of any number).

Ex. 1 : Find the cube of  728 ( 728³= ? )

Step 1 : Split the number as like i.e  7 – 28 or 72 – 8.

Here we take 72 – 8 .

Step 2 : Divide the 1st part by 2nd part. i.e 72/8 = 9. Here we can take a = 8 , b= 9 , c = 8³ = 512

Step 3 : Cube of 1st part c = 8 x 8  x 8 = 512. Here Take last digit in answer and remaining value 51 to be add to next step.

i.e Ans :  _ _ _ _ 2  and 51 is to be add in the next step.

Step 4 : 3 bc + 51= (3 x 9 x 512) +51=  13824 + 51 = 13875 . Here Take lost digit into the next digit in answer and remaining value 1387 to be add to next step.

i.e Ans :  _ _ _ 5 2  and 1387 is to be add in the next step.

Step 5 : 3 b² c +13875= (3 x 9 x 9 x 512) +1387= 124416 + 1387 = 125803 . Here Take lost digit into the next digit in answer and remaining value 12580 to be add to next step.

i.e Ans :  _ _ _3 5 2  and  12580 is to be add in the next step.

Step 6 : b³ c +12580= ( 9 x 9 x 9 x512) +12580= 373248 + 12580 = 385828. Here Take this value into the answer

i.e Ans :  385828352.

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