CLASS-7
FINDING CUBE ROOT OF DECIMAL NUMBERS BY COMMON FACTORIZATION METHOD
FINDING CUBE ROOT OF DECIMAL NUMBERS BY COMMON FACTORIZATION METHOD -
The common factorization method involves breaking the number into its prime factors and then grouping them into triples. Here’s a step-by-step guide:-
Step.1:- Convert the Decimal to a Fraction
If the number is a decimal, express it as a fraction.
For example, let’s find ∛0.008
8
0.008 = --------
1000
Step.2:- Prime Factorization of Numerator and Denominator
Factorize 8 and 1000 into their prime factors:
8 = 2 × 2 × 2 = 2³
1000 = 10 x 10 x 10 = 2³ x 5³
Step.3:- Apply the Cube Root to Both Numerator and Denominator
∛8 ∛2³ 2 2
∛0.008 = -------- = ------------ = --------- = ------ = 0.2
∛1000 ∛2³ x ∛5³ 2 x 5 10
Final Answer :- ∛0.008 = 0.2 (Ans.)
Another Example: ∛0.027
Ans.)
- Convert to Fraction:-
27
0.027 = --------
1000
2. Factorize:-
27 = 3³ and 1000 = 10³
3. Apply Cube Root:-
∛27 ∛3³ 3
∛0.027 = --------- = -------- = ------- = 0.3
∛1000 ∛10³ 10
Final Answer:- ∛0.027 = 0.3 (Ans.)
Example.3) Find the cube root of 19.683 by the common factorization method.
Ans.)
