Which of the following is between π

Question

 and  11−−√
?(1 point)
Responses

8–√
Start Root 8 End Root

7–√
Start Root 7 End Root

12−−√
Start Root 12 End Root

10−−√

Answer 1

To determine which of the given options is between \(\pi\) and \(\sqrt{11}\), we first need to approximate the values of \(\pi\) and \(\sqrt{11}\).

• \(\pi \approx 3.14\)
• \(\sqrt{11} \approx 3.32\) (because \(3.32^2 \approx 11\))

Next, let's approximate the given options:

1. \(\sqrt{8} \approx 2.83\)
2. \(\sqrt{7} \approx 2.65\)
3. \(\sqrt{12} \approx 3.46\)
4. \(\sqrt{10} \approx 3.16\)

Now we will check which of these values falls between \( \pi \approx 3.14\) and \(\sqrt{11} \approx 3.32\):

• \(\sqrt{8} \approx 2.83\) (not between \(\pi\) and \(\sqrt{11}\))
• \(\sqrt{7} \approx 2.65\) (not between \(\pi\) and \(\sqrt{11}\))
• \(\sqrt{12} \approx 3.46\) (not between \(\pi\) and \(\sqrt{11}\))
• \(\sqrt{10} \approx 3.16\) (between \(\pi\) and \(\sqrt{11}\))

Thus, the only option that falls between \(\pi\) and \(\sqrt{11}\) is \(\sqrt{10}\).