Hi, my question is that can we find a cube root of a number by long division method and why please tell me
Answers
Answer:
CUBE ROOTS BY DIVISION METHOD
Consider the numbers 64 and 216 resolving 64 and 216 into prime factors.
64 = 2x2x2x2x2x2
216=2x2x2x3x3x3
In both these cases each factor appears three times that is the prime factors can be grouped in triples, thus if a number can be expressed as a product of three equal factors. Then it is said to be a perfect cube or cubic number.
So a cube number is obtained when a number is multiplied by itself for three times.
That is cube of a number is A x A x A = A
3
suppose a cube is formed with 125 unit cubes what could be side of the cube?
Let us assume, the length of the side to be ‘ x ’ .
.
.
. 125 = x
3
To find the side of a cube it is necessary to find a number whose cube is 125.
Therefore, finding the number whose cube is known is called finding the cube root. It is the inverse operation of cubing.
As 5
3
= 125 then 5 is called cube root of 125.We write =5 the symbol e denotes cube root. Hence a number ‘x’ is the cube root of another number y.
If y=x
3
then x =
Let us find the cube root of 4096
Resolving 4096 into prime factors,
we get
4096 = 2x2x2x2x2x2x2x2x2x2x2x2
= =2x2x2 x2 =16
Finding cube root by division method
Let us find cube root of 1331 by division method
Step 1: Start making groups of three digits starting from the unit place.
Step 2: Find the largest number whose cube is less than or equal to the first group of digits from left ( ie 1) Take this number as the divisor and the quoient.
Step 3: Subtract the cube of the number from first group or single digit (ie 1-1=0) .
Step 4: Brng down the second group (ie 331) to the right of the remainder this becomes the new dividend (ie 331).
Step 5: From the next possible divisor triple the quotient (ie 1x3=3) and write a box on its right.
Step 6: Guess the largest possible digit to fill box in such a way take the cube of the new divisor take the unit value of cube number in unit digits (ie 1
3
=1) then the product of this number and previous divisor multiply with the new quotient (ie 1x3=3 then 3x11=33) add the remain digts we loft from cube of new divisor is equal to or less then the new dividend.
Step 7: By subtracting we get the remainder zero. The final quotient 11 is the cube root
.
.
. =11.