Question

what is the best estimate for \\(\sqrt{34}\\) to the nearest whole number?\
\\(\bigcirc\\) a 35\
\\(\bigcirc\\) b 13\
\\(\bigcirc\\) c 17\
\\(\bigcirc\\) d 8\
\\(\bigcirc\\) e 6

Explanation:

Step1: Recall perfect squares around 34

We know that \(5^2 = 25\) and \(6^2 = 36\). So, \(\sqrt{25}=5\) and \(\sqrt{36}=6\).

Step2: Compare 34 with 25 and 36

Since \(25<34<36\), taking square roots (which is a monotonic function for non - negative numbers), we have \(\sqrt{25}<\sqrt{34}<\sqrt{36}\), that is \(5 < \sqrt{34}<6\).

Step3: Determine the nearest whole number

Now, we calculate the distance of 34 from 25 and 36. The distance from 34 to 25 is \(34 - 25=9\), and the distance from 36 to 34 is \(36 - 34 = 2\). Since 34 is closer to 36 than to 25, \(\sqrt{34}\) is closer to 6 than to 5.

Answer:

E. 6