Simplify 54−−√3 .

Question

Note: You will find the option to add a cubic root symbol in the Algebra ( ×
) keyboard.

Answer 1

To simplify 54^(1/3):

Since the cube root of 54 is not an integer, we can write it as a simplified radical expression.

Let's find the prime factorization of 54:
54 = 2 × 3 × 3 × 3 = 2 × 3^3

Now we can write 54^(1/3) as (2 × 3^3)^(1/3):

Using the property (a × b)^(1/n) = a^(1/n) × b^(1/n), we can simplify it as follows:

(2 × 3^3)^(1/3) = 2^(1/3) × (3^3)^(1/3)

Since (3^3)^(1/3) = 3, we have:

2^(1/3) × (3^3)^(1/3) = 2^(1/3) × 3 = 3 × 2^(1/3)

Hence, 54^(1/3) simplifies to 3 × 2^(1/3).