LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

FINDING CUBE ROOT BY PRIME FACTORIZATION METHOD

__To Find the Cube Root by Prime Factorization __

**Step.1) Express the number as a product
of prime factors.**

**Step.2) Make Triplets of equal prime
factors.**

**Step.3) Take one Factor from each
triplet and multiply them.**

**We can also express the number as a product of powers of
prime factors, then dividing each index by 3 and multiplying the obtained
factors we can find the cube root.**

**Example.1) Find the cube root of 216000**

**So, 216000 ****= 10 X 10
X 10 X 3 X 3 X 3 X 2 X 2 X 2**

**= (10 X 10 X 10) X (3 X 3 X 3) X
(2 X 2 X 2)**

**= 10ᶟ X 3ᶟ X 2ᶟ**

**So, ∛216000 = ∛(10ᶟ X 3ᶟ X 2ᶟ)**

**= ∛10ᶟ X ∛3ᶟ X ∛2ᶟ**

**= 10 X 3 X 2 = 60**

**So, cube root of 216000 is 60 (Ans.)**

**Example.2) Find the cube root of 42875**

**So, 42875 = 5 X 5 X 5 X 7 X 7 X 7 **

** = (5 X 5 X 5) X (7 X 7 X 7) **

** = 5ᶟ X 7ᶟ **

**So, ∛42875 = ∛(5ᶟ X 7ᶟ )**

** = ∛5ᶟ X ∛7ᶟ**

** = 5 X 7 = 35 **

**So, the obtained cube root of 42875 is 35 (Ans.)**