Question

complete the following statement. use the integers that are closest to the number in the middle.
□ < √6 < □

Explanation:

Step1: Recall perfect squares

We know that \(2^2 = 4\) and \(3^2 = 9\).

Step2: Compare with \(\sqrt{6}\)

Since \(4<6<9\), taking square roots (and since square root is an increasing function for non - negative numbers), we get \(\sqrt{4}<\sqrt{6}<\sqrt{9}\), which simplifies to \(2 < \sqrt{6}<3\).

Answer:

\(2<\sqrt{6}<3\)