We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
315
1
avatar+603 

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
avatar+101322 
+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

 Apr 21, 2018

16 Online Users

avatar
avatar