What is the cube root of 19683 using the factorization method?

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answer is A.

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Detailed Solution

The given number is 19683.
Now, using prime factorization, express 19683 as the product of two prime factors, and create similar factor pairs where the two factors in each pair are equal.

⇒ 19683 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3

Group the factors in cubes. The quantity is a perfect cube as there are no factors left behind after grouping (triples).
Here,

⇒ 196833 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 3 ⇒ 196833 = 33 × 33 × 33 3

⇒ 196833 = 3 × 3 × 3 ⇒ 196833 = 27

So, the cube root of 19683 =

27.

Therefore, option 1 is correct.

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