To determine between which two integers the value of [tex]\(\sqrt{10}\)[/tex] lies, let's breakdown our steps clearly.
1. Calculate the exact value of [tex]\(\sqrt{10}\)[/tex]:
[tex]\[
\sqrt{10} \approx 3.1622776601683795
\][/tex]
2. Identify the integer part of [tex]\(\sqrt{10}\)[/tex]:
- The integer part of [tex]\(3.1622776601683795\)[/tex] is [tex]\(3\)[/tex].
3. Determine the two consecutive integers:
- The integer part [tex]\(3\)[/tex] suggests that [tex]\( \sqrt{10}\)[/tex] lies between [tex]\(3\)[/tex] and the next integer, which is [tex]\(4\)[/tex].
To summarize, [tex]\(\sqrt{10}\)[/tex] lies between the integers [tex]\(3\)[/tex] and [tex]\(4\)[/tex].
