Question

Which point best approximates StartRoot 45 EndRoot?

A number line going from 0 to 9. Point A is slightly to the right of 2, point B is to the left of 5, point C is to the left of 7, and point D is to the right of 7.
A
B
C
D

Answer 1

To approximate \(\sqrt{45}\), let's first find the perfect squares around 45.

We know:
- \(6^2 = 36\)
- \(7^2 = 49\)

This means:
\[
6 < \sqrt{45} < 7
\]

To get a better approximation, we can consider values between 6 and 7. We can also compute \(\sqrt{45}\) more directly:

\[
\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}
\]

Now, we will find an approximate value for \(\sqrt{5}\). The value of \(\sqrt{5}\) is approximately 2.236. Thus:
\[
3\sqrt{5} \approx 3 \times 2.236 = 6.708
\]

So, \(\sqrt{45} \approx 6.708\).

Now, let's analyze the points on the number line:
- Point A is slightly to the right of 2.
- Point B is to the left of 5.
- Point C is to the left of 7.
- Point D is to the right of 7.

Since \(\sqrt{45} \approx 6.708\), the best point that represents this value on the number line would be point C, which is slightly to the left of 7.

Therefore, the best approximation for \(\sqrt{45}\) is:
**C**.