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

1 Answer
Nov 7, 2016

Answer:

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