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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?

gueesstt  Apr 21, 2018
 #1
avatar+87293 
+1

\(1 \le a \le 10$ and $1 \le b \le 36 \)

 

\(\sqrt{a + \sqrt{b}} \)

 

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

 

 

cool cool cool

CPhill  Apr 21, 2018

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