To solve the problem of determining the integers that are closest to [tex]\(\sqrt{42}\)[/tex], we need to identify the integers that are immediately less than and greater than [tex]\(\sqrt{42}\)[/tex].
1. Calculate the square root of 42:
The square root of 42 is approximately [tex]\(6.48074069840786\)[/tex].
2. Determine the closest integers:
- The integer closest to [tex]\(6.48074069840786\)[/tex] that is smaller is [tex]\(6\)[/tex].
- The integer closest to [tex]\(6.48074069840786\)[/tex] that is larger is [tex]\(7\)[/tex].
3. Formulate the inequality:
Given these integers, we can complete the inequality statement as follows:
[tex]\[
6 < \sqrt{42} < 7
\][/tex]
Therefore, the statement completed with these integers is [tex]\(6 < \sqrt{42} < 7\)[/tex].
