To approximate the value of [tex]\(\sqrt{10}\)[/tex], we need to find two consecutive whole numbers between which [tex]\(\sqrt{10}\)[/tex] falls.
1. Let's start by evaluating the squares of some whole numbers:
- [tex]\(3^2 = 9\)[/tex]
- [tex]\(4^2 = 16\)[/tex]
2. Now, we need to determine between which two whole numbers [tex]\(\sqrt{10}\)[/tex] falls by comparing it to these squares:
- Since [tex]\(\sqrt{10} > \sqrt{9}\)[/tex] and [tex]\(\sqrt{10} < \sqrt{16}\)[/tex], we can conclude that [tex]\(\sqrt{10}\)[/tex] lies between 3 and 4.
Therefore, the value of [tex]\(\sqrt{10}\)[/tex] is between 3 and 4.
