# How do you know whether sqrt38 is is closer to 6 or 7 without using a calculator?

Nov 7, 2016

Closer to 6

#### Explanation:

It is true that we can look at this and think the answer is closer to 6 but can we prove it??
Look at the half way point 6.5
6.5x 6.5
(6x 6.5 ==39, 0.5x 6.5= 3.25)
${6.5}^{2} = 42.25$

38<42.25 so $\sqrt{38}$. < halfway between 6 and 7