Q.Write the set $B = \{x : x \in \mathbb{N}, x^2 < 30\}$ in roster form.

Set-builder form gives a rule; to convert to roster form, test natural numbers one by one against the rule until it stops holding.

Testing: $1^2=1$, $2^2=4$, $3^2=9$, $4^2=16$, $5^2=25$ — all less than 30. But $6^2=36$, which is not less than 30.

Step 1 — Understand the rule. $x$ must be a natural number ($x \in \mathbb{N} = \{1, 2, 3, \dots\}$) satisfying $x^2 < 30$.

Step 2 — Test successive natural numbers.

• $x=1$: $1^2 = 1 < 30$ ✓
• $x=2$: $2^2 = 4 < 30$ ✓
• $x=3$: $3^2 = 9 < 30$ ✓
• $x=4$: $4^2 = 16 < 30$ ✓
• $x=5$: $5^2 = 25 < 30$ ✓
• $x=6$: $6^2 = 36 \not< 30$ ✗ — fails, and since $x^2$ only grows larger as $x$ increases, no larger $x$ can satisfy the rule either.

Step 3 — Collect the values that passed. $x = 1, 2, 3, 4, 5$.