Question

Represent the following set in Roster form

C = {x : x is perfect cube, 27 < x < 216}

Answer 1

To represent the set C = {x : x is a perfect cube, 27 < x < 216} in Roster form, we need to list the perfect cubes that exist strictly between 27 and 216.

Identify the cubes of integers:

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Apply the condition 27 < x < 216:

Since the condition is strictly greater than 27 and strictly less than 216, we exclude 27 and 216.

The perfect cubes that satisfy this condition are 64 and 125.

Roster Form:

C = {64, 125}