Question

complete the following statement. use the integers that are closest to the number in the middle.
□ < √116 < □

Explanation:

Step1: Find perfect squares around 116

We know that \(10^2 = 100\) and \(11^2 = 121\). Also, \(100<116<121\).

Step2: Take square roots

Taking square roots of each part of the inequality \(100 < 116 < 121\), we get \(\sqrt{100}<\sqrt{116}<\sqrt{121}\). Since \(\sqrt{100} = 10\) and \(\sqrt{121}=11\), we have \(10 < \sqrt{116}<11\).

Answer:

\(10 < \sqrt{116} < 11\)