Question

without using a calculator, determine which whole number \\(\sqrt{70}\\) is closest to.

\\(\bigcirc\\) 7

\\(\bigcirc\\) 8

\\(\bigcirc\\) 9

Explanation:

Step1: Find perfect squares around 70

We know that \(8^2 = 64\) and \(9^2 = 81\). So, \(\sqrt{64}=8\) and \(\sqrt{81}=9\). Since \(64<70<81\), \(\sqrt{70}\) is between 8 and 9.

Step2: Compare distances

Calculate the distance from 70 to 64 and from 81 to 70. The distance from 70 to 64 is \(70 - 64 = 6\), and the distance from 81 to 70 is \(81 - 70 = 11\). Since 6 is less than 11, 70 is closer to 64 than to 81. So, \(\sqrt{70}\) is closer to 8.

Answer:

8 (corresponding to the option "8")