To determine between which two consecutive whole numbers [tex]\(\sqrt{19}\)[/tex] lies, we will follow these steps:
1. First, let's identify the two whole numbers whose squares are closest to 19 without exceeding it. We will denote these whole numbers as [tex]\( n \)[/tex], such that [tex]\( n^2 \leq 19 < (n+1)^2 \)[/tex].
2. Calculating the squares of consecutive whole numbers:
- [tex]\( \sqrt{4^2} = 16 \)[/tex]
- [tex]\( \sqrt{5^2} = 25 \)[/tex]
- We see that [tex]\( 16 < 19 < 25 \)[/tex].
3. Therefore, the two whole numbers that [tex]\(\sqrt{19}\)[/tex] lies between are 4 and 5.
To fill out the answer:
Since [tex]\(\sqrt{16} = 4\)[/tex] and [tex]\(\sqrt{25} = 5\)[/tex], it is known that [tex]\(\sqrt{19}\)[/tex] is between 4 and 5.
