Answer :
30.00 i think. but 30 is a whole number so its not really being rounded
30 = (5 + h)^2
30 = 25 + 10h + h^2
5 = 10h + h^2
0 < h < 1
If 0 < h < 1, then 0 < h^2 < 1 as well
4 = 10h , 5 = 10h
0.4 = h , 0.5 = h
0.4 < h < 0.5
5.5^2 = 30.25
5.4^2 = 29.16
30 = (5.4 + h)^2
30 = 29.16 + 10.8h + h^2
0 < h < 0.1
0 < h^2 < 0.01
0.84 = 10.8h + h^2
0.83 = 10.8h , 0.84 = 10.8h
83/1080 = h , 84/1080 = h
83/1080 < h < 84/1080
5.4 + 83/1080 =>
5.476851851851....
5915/1080
1183/216
(1183/216)^2 = 29.995906207133058984910836762689
Ah, that's close enough.
5.47685
30 = 25 + 10h + h^2
5 = 10h + h^2
0 < h < 1
If 0 < h < 1, then 0 < h^2 < 1 as well
4 = 10h , 5 = 10h
0.4 = h , 0.5 = h
0.4 < h < 0.5
5.5^2 = 30.25
5.4^2 = 29.16
30 = (5.4 + h)^2
30 = 29.16 + 10.8h + h^2
0 < h < 0.1
0 < h^2 < 0.01
0.84 = 10.8h + h^2
0.83 = 10.8h , 0.84 = 10.8h
83/1080 = h , 84/1080 = h
83/1080 < h < 84/1080
5.4 + 83/1080 =>
5.476851851851....
5915/1080
1183/216
(1183/216)^2 = 29.995906207133058984910836762689
Ah, that's close enough.
5.47685