To determine which square root is between 4 and 5, we'll evaluate the square roots of the given numbers and see which one lies within the interval (4, 5).
1. [tex]\(\sqrt{10}\)[/tex]:
The square root of 10 is approximately [tex]\(3.162\)[/tex]. Since [tex]\(3.162\)[/tex] is less than [tex]\(4\)[/tex], [tex]\(\sqrt{10}\)[/tex] is not between 4 and 5.
2. [tex]\(\sqrt{14}\)[/tex]:
The square root of 14 is approximately [tex]\(3.742\)[/tex]. Since [tex]\(3.742\)[/tex] is still less than [tex]\(4\)[/tex], [tex]\(\sqrt{14}\)[/tex] is not between 4 and 5.
3. [tex]\(\sqrt{24}\)[/tex]:
The square root of 24 is approximately [tex]\(4.899\)[/tex]. Since [tex]\(4.899\)[/tex] is greater than [tex]\(4\)[/tex] and less than [tex]\(5\)[/tex], [tex]\(\sqrt{24}\)[/tex] is indeed between 4 and 5.
4. [tex]\(\sqrt{32}\)[/tex]:
The square root of 32 is approximately [tex]\(5.657\)[/tex]. Since [tex]\(5.657\)[/tex] is greater than [tex]\(5\)[/tex], [tex]\(\sqrt{32}\)[/tex] is not between 4 and 5.
Based on these evaluations, the square root that lies between 4 and 5 is:
[tex]\[
\boxed{\sqrt{24}}
\][/tex]
