CUBE ROOT OF A NUMBER BY DIVISION METHOD

FINDING CUBE ROOT BY DIVISION METHOD

STEPS INVOLVED IN FINDING THE CUBE ROOT

To understand the process of finding the cube root of a number by the division method, let us take the number 13824 and try to find the cube root of this number.

STEP 1 – Let us take the digits of the number into groups of threes, starting from the right to the left i.e., from the unit place. In our example, the groups are ‘824’ and ‘13’.

STEP 2 – We need to find the number whose cube is equal to or less than 13 and subtract the cube of that number from the first group from left to right. In our example, that number is 2 because its cube is ‘8’ which is less than 13. We will subtract it from 13, which is our first group from left to right. So, 2 becomes the first quotient.

STEP 3 – After subtraction, we will bring down the next group. So, we will bring down ‘824’ and the number that will be formed is 5824.

STEP 4 – Now, we have to find the other digit of the quotient. To find the second digit of the quotient, we will use the following expression –

[(10a + b)×30a + b²] × b

where      a = first digit of the quotient,

b = second digit of the quotient

(10a + b) = the two-digit number formed by joining a and b.

In our example, the value of a = 2, so the expression = [30×2(10×2 + b) + b²] × b.

We can simplify this expression as [60(20 + b)+ b²] × b.

STEP 5 – We will use the trial and error method for determining the value of ‘b’ and the value of expression must be less than or equal to the number formed in STEP 3. In our example, it must be equal to or less than 5,824. The trial and error method is as follows –

b = 1, (60 × 21 + 1²) × 1 = 1261

b = 2, (60 × 22 + 2²) × 2 = 2648

b = 3, (60 × 23 + 3²) × 3 = 4167

b = 4, (60 × 24 + 4²) × 4 = 5824

We can see that when b = 4, then the value of the expression is equal to 5824.

Therefore, 24 is the cube root of 13824. It means that when 24 is multiplied three times by itself,  the resultant number is 13824.

In this way, we can find the cube root of the number. We generally apply the prime factorisation method to find the cube root but when the number is large, the division method becomes easy as compared to the prime factorisation method for finding the cube root of the number. The division method can be applied to both the large and the small numbers.