Find the length in segment ag in the spiral shown

You can solve the problem using Pythagoras theorem a^2 + b^2 = c^2
If AB= a and BC=b, then AC would be c. Since AB and BC are given, we can find the length of AC. The calculation would be:
c^2=  a^2 + b^2 
AC^2=  AB^2 + BC^2 
AC^2=  2^2 + 1^2 
AC^2= 4+1 = 5

Using the same formula again you can determine AD length
c^2=  a^2 + b^2 
AD^2=  AC^2 + CD^2 
AD^2 = 5 + 1^2= 6

Repeating the process again, you will find out that 
AE^2= 7
A.F^2=8
AG^2=9

Then, AG would be: √9= 3