# Appearance may deceive.

**\(p\)** and **\(q\)** are real numbers where

**\(p=\sqrt{\frac{17}{2}+6\sqrt{2}}+\sqrt{\frac{17}{2}-6\sqrt{2}}\)**

and

**\(q=\sqrt{\frac{17}{2}+6\sqrt{2}}-\sqrt{\frac{17}{2}-6\sqrt{2}}\)**.

Then **\(\sqrt{2} (pq)^{-1}\)** can be expressed as **\(\frac{a}{b}\)**, where **\(a\)** and **\(b\)** are coprime integers.

What is the value of **\(a+b\)**?