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Complete the following statement. Use the integers that are closest to the number in the middle.

[tex]\[ \square \ \textless \ \sqrt{42} \ \textless \ \square \][/tex]


Sagot :

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].