Question

between which two consecutive whole numbers does \\(\sqrt{89}\\) lie? fill out the sentence below to justify your answer and use your mouse to drag \\(\sqrt{89}\\) to an approximately correct location on the number line. \\(\sqrt{89}\\) (number line with 0 to 10) answer attempt 1 out of 2 since \\(\sqrt{\square} = \square\\) and \\(\sqrt{\square} = \square\\) it is known that \\(\sqrt{89}\\) is between \\(\square\\) and \\(\square\\).

Explanation:

Step1: Find the perfect square less than 89

We know that \(9^2 = 81\), so \(\sqrt{81}=9\).

Step2: Find the perfect square greater than 89

We know that \(10^2 = 100\), so \(\sqrt{100}=10\).

Step3: Compare with \(\sqrt{89}\)

Since \(81<89<100\), taking square roots (and since square root is an increasing function), we have \(\sqrt{81}<\sqrt{89}<\sqrt{100}\), which means \(9 < \sqrt{89}<10\).

Answer:

Since \(\sqrt{\boldsymbol{81}}=\boldsymbol{9}\) and \(\sqrt{\boldsymbol{100}}=\boldsymbol{10}\) it is known that \(\sqrt{89}\) is between \(\boldsymbol{9}\) and \(\boldsymbol{10}\).