Question

complete the following statement. use the integers that are closest to the middle.
□ < √2 < □
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Explanation:

Step1: Recall square of integers

We know that \(1^2 = 1\) and \(2^2=4\). Also, \((\sqrt{2})^2 = 2\).

Step2: Compare with square roots

Since \(1^2<(\sqrt{2})^2 < 2^2\) and for positive numbers, if \(a^2 < b^2\) then \(a < b\) (where \(a,b>0\)). So \(1<\sqrt{2}<2\).

Answer:

\(1 < \sqrt{2} < 2\)