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

Apr 21, 2018

#1
+98044
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$$1 \le a \le 10 and 1 \le b \le 36$$

$$\sqrt{a + \sqrt{b}}$$

b  is  only an integer when  b  = 1, 4, 9, 16, 25 , 36

The possible pairs of (a, b)  are

(1, 9)

(2, 4)

(3, 36)

(4, 25)

(5, 16)

(6, 9)

(7, 4)

(8, 1)

(10, 36)

So.....nine possible ordered pairs

Apr 21, 2018