**2016 JMO Prelim 1.** Calculate the value of and answer in the form of an integer.

**Two obvious facts that help get us started:**

- That the answer is an integer should tell us that the expression inside the square root is a perfect square.
- . Perhaps we should generalise and see if is a perfect square.

* Let’s try to match this to a perfect square expression.* The and terms suggest that there should be and terms in the square, i.e.:

for some . Let’s expand the above and see what could be:

It’s clear that fulfills the above, i.e. for any and ,

Substituting and , we have

The answer is **11221**. **Done!**

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