Question

what two whole numbers is \\(\sqrt{67}\\) between? *enter only numbers in the blanks below! (1 point) \\(\sqrt{67}\\) is between \\(\square\\) and \\(\square\\), but it closer to \\(\square\\).

Explanation:

Step1: Find perfect squares around 67

We know that \(8^2 = 64\) and \(9^2 = 81\). Since \(64<67<81\), taking square roots (and since square root is an increasing function), we have \(\sqrt{64}<\sqrt{67}<\sqrt{81}\), so \(8 < \sqrt{67}<9\).

Step2: Determine closeness

Calculate the differences: \(67 - 64=3\) and \(81 - 67 = 14\). Since \(3<14\), \(\sqrt{67}\) is closer to \(8\) (because the difference between 67 and \(8^2 = 64\) is smaller than the difference between 67 and \(9^2=81\)).

Answer:

\(\sqrt{67}\) is between \(8\) and \(9\), but it closer to \(8\).