Question

1. which point on the number line represent √42? (image shows a number line with ticks at 4, 5, 6, 7, 8, 9, 10, 11, and points labeled p (between 4–5), q (between 6–7), r (between 8–9), s (between 10–11), with multiple-choice options p, q, r, s as circles.)

Explanation:

Step1: Find perfect squares around 42

We know that \(6^2 = 36\) and \(7^2 = 49\). So, \(\sqrt{36}<\sqrt{42}<\sqrt{49}\), which means \(6 < \sqrt{42}<7\).

Step2: Analyze the number line points

• Point \(p\) is around 4.5 (between 4 and 5), so not in \(6 - 7\).
• Point \(q\) is between 6 and 7 (since it's between 6 and 7 on the number line).
• Point \(r\) is around 8.5 (between 8 and 9), not in \(6 - 7\).
• Point \(s\) is around 10.5 (between 10 and 11), not in \(6 - 7\).

Since \(\sqrt{42}\) is between 6 and 7, the point \(q\) represents \(\sqrt{42}\).

Answer:

q