Question

between which two consecutive whole numbers does \\(\sqrt{60}\\) lie? fill out the sentence below to justify your answer and use your mouse to drag \\(\sqrt{60}\\) to an approximately correct location on the number line.

answer attempt 1 out of 2

since \\(\sqrt{\square} = \square\\) and \\(\sqrt{\square} = \square\\) it is known that \\(\sqrt{60}\\) is between \\(\square\\) and \\(\square\\).

Explanation:

Step1: Find the perfect square less than 60

We know that \(7^2 = 49\), so \(\sqrt{49} = 7\).

Step2: Find the perfect square greater than 60

We know that \(8^2 = 64\), so \(\sqrt{64} = 8\).

Step3: Compare with \(\sqrt{60}\)

Since \(49 < 60 < 64\), taking square roots (and since square root is an increasing function for non - negative numbers), we have \(\sqrt{49}<\sqrt{60}<\sqrt{64}\), which means \(7 < \sqrt{60}<8\).

Answer:

Since \(\sqrt{\boldsymbol{49}}=\boldsymbol{7}\) and \(\sqrt{\boldsymbol{64}}=\boldsymbol{8}\) it is known that \(\sqrt{60}\) is between \(\boldsymbol{7}\) and \(\boldsymbol{8}\).