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

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

A cube of a number means that 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 a calculator. It will help all students to do fast calculations in their regular and commutative exams.

First, remember the 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 the cube of that number

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

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

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

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

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 the lost digit into the answer’s last place and the remaining value to be added to the next step.

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

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

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

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

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

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

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 the 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 the last digit in the answer and the remaining value 51 to be added to the next step.

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

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

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

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

i.e Ans: _ _ _3 5 2 and 12580 are to be added 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.