Answer:
Using binomial expansion,
√
a
2
+
b
=
a
(
1
+
b
a
2
)
1
2
=
a
(
1
+
1
2
b
a
2
)
, nearly.
Here, choose a = 66 and b = 44.
Now,
√
4400
=
√
66
2
+
44
=
√
66
2
+
44
=
66
(
1
+
44
66
2
)
1
2
66
(
1
+
1
2
(
44
66
2
)
)
=
66
(
1
+
1
198
)
=
66
+
1
3
=
66.33
, nearly.
Note that the error is of order 66(1/198)^2=O(.002), nearly.
Explanation:
