Question

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

Answer 1

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 `sqrt38`. < halfway between 6 and 7