Final answer:
Set B in roster form is {3, 4, 5, 6, 7, ...}, including all natural numbers starting from 3 whose squares are greater than 5.
Step-by-step explanation:
The student's question involves expressing a set in roster form. The given set is B = x ∈ ℕ and x^2 > 5, where ∈ means 'is an element of', ℕ stands for the set of natural numbers, and x^2 represents the square of x. To find the elements of set B, we need to discover the natural numbers that, when squared, give a result greater than 5.
Starting from the smallest natural number, 1, and checking subsequent numbers individually:
1^2 = 1 (not greater than 5)
2^2 = 4 (not greater than 5)
3^2 = 9 (greater than 5)
So the first element in our set B that satisfies x^2 > 5 is 3. Continuing this pattern:
4^2 = 16 (greater than 5)
5^2 = 25 (greater than 5)
... and so on for all larger natural numbers.
Therefore, the set B in roster form is {3, 4, 5, 6, 7, ...}, which illustrates that the set contains all natural numbers starting from 3 and increasing without bound.