Second 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 $N$.

One of the other two inspiring methods of solving the above question will be discussed in this post.

When we're asked to compare two quantities, like in this instance, we have $M$ and $N$. But that doesn't restrict us in working and considering only with the linear power of  $M$ and $N$.