Question

complete the following statement. use the integers that are closest to the number in the middle. \\(square < sqrt{107} < square\\)

Explanation:

Step1: Find perfect squares around 107

We know that \(10^2 = 100\) and \(11^2 = 121\).

Step2: Compare with \(\sqrt{107}\)

Since \(100<107<121\), taking square roots (and noting that square root is an increasing function), we get \(\sqrt{100}<\sqrt{107}<\sqrt{121}\), which simplifies to \(10 < \sqrt{107}< 11\).

Answer:

\(10 < \sqrt{107}< 11\) (So the first box is 10 and the second box is 11)