Question

Estimate square root of 245 to the nearest hundredths place

Answer 1

Again, we assume no calculators are allowed, all in the head.
You can cheat with pen and paper, but that defeats the challenge.

Look at 245, it is close to 240.
We know that 15*16=240
so
15.5^2=15*16+0.5^2=240.25

Use Newton's method, with x0=15.5
x1=15.5-(15.5^2-245)/(2*15.5)
=15.5+4.75/31
=15.5+0.153
=15.653
=15.65 (to the hundredth)
Exact square root 15.6524

Answer 2

The square root of 245 to the nearest hundredths place is 15.65.

Hope this helped!