Question

complete the following statement. use the integers that are closest to the number in the middle.
6 < √33 < 7

Explanation:

Step1: Square the integers

Calculate \(6^2 = 36\) and \(7^2=49\), and also note that \((\sqrt{33})^2 = 33\).

Step2: Compare the values

Since \(33<36\) and \(33 < 49\), and we know that the square - root function \(y = \sqrt{x}\) is an increasing function. So \(\sqrt{33}<6\) is wrong, and \(\sqrt{33}<7\) is correct. Also, \(5^2=25\) and \(33>25\), so \(5<\sqrt{33}<6\).

Answer:

\(5 < \sqrt{33}<6\)