SOLUTION: If 1 ≤ a ≤ 10 and 1 ≤ b ≤ 36, for how many ordered pairs of integers (a, b) is square root ( a + square root b) an integer?

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Question 203335: If 1 ≤ a ≤ 10 and 1 ≤ b ≤ 36, for how many ordered pairs of integers (a, b) is
square root ( a + square root b) an integer?
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
In order for to be an integer, must be a perfect square. And for to be a perfect square, must be an integer. And finally, in order for to be an integer, b must be a perfect square.

So we'll start by checking possible values for "b": perfect squares between 1 and 36 (inclusive). And we will then see if we can find an "a", between 1 and 10 (inclusive) which makes the rest of the expression work out as desired.
So the solutions as ordered pairs:
(3, 1)
(8, 1)
(2, 4)
(7, 4)
(1, 9)
(6, 9)
(5, 16)
(4, 25)
(3, 26)
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