F$1 \le a \le 10$ and $1 \le b \le 36$, for how many ordered pairs of integers $(a, b)$ is $\sqrt{a + \sqrt{b}}$ an integer?

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Consider expression . If this expression becomes an integer, then b=4,9,16,25, because then 2,3,4,5, respectively. In other cases is not integer and thus the expression also is not integer.

1. b=4, then . Here a=2,7 (in other cases is not integer). When a=2, and when a=7, .

2. b=9, then a=6 and .

3. b=16, then a=5 and .

4. b=25, then a=4 and .

(2,4), (7,4), (6,9), (5,16), (4,25).