Third Heuristic Method In Solving Problem: Compare $M$ and $N$.

Given that $p,\,q,\,r,\,s,\,a,\,b$ are positive real numbers with $M=\sqrt{ap+br}\cdot \sqrt{\dfrac{q}{a}+\dfrac{s}{b}}$ and $N=\sqrt{pq}+\sqrt{rs}$. Compare $M$ and $N$.

The third inspiring methods of solving the above question will be discussed in this post.

It's solved by one Indian genius, a math friend of mine who compared the quantities between $M^4$ and $N^4$:

He first noticed