Which point best represents \sqrt{10}on a number line?

Question

The number line between 0 and 10 shows points A, B, C, and D. The point A is at 2, B is between 3 and 4, C is at 5, and D is at 10.

A.
point A

B.
point B

C.
point C

D.
point D

Answer 1

To determine the approximate location of \(\sqrt{10}\) on the number line, we first need to calculate the square root of 10.

1. We know that \(3^2 = 9\) and \(4^2 = 16\). This means \(\sqrt{10}\) is between 3 and 4, since 9 < 10 < 16.
2. Next, we can estimate \(\sqrt{10}\) to be approximately 3.16 (since \(3.16^2 \approx 10\)).

Looking at the points on the number line:

• Point A is at 2.
• Point B is between 3 and 4, which seems to be where \(\sqrt{10}\) (approximately 3.16) would fall.
• Point C is at 5.
• Point D is at 10.

Based on this information:

The best choice that represents \(\sqrt{10}\) on the number line is:

B. point B