Evaluating Integral parts of continued conjugates

Solution will be short but I'll give it my best shot. (Difficult to type in an iPad)

$\displaystyle P>2((\sqrt{10001}-\sqrt{10000})+(\sqrt{10000}-\sqrt{9999})+....+(\sqrt{3}-\sqrt{2}))\approx197.1816$

Similarly,

$\displaystyle P<2(\sqrt{10000}-\sqrt{1})=198$

So $\displaystyle 197<P<198$

And the Integral Part = $\boxed{197}$

I have no idea how to approach this problem. I solved it by inserting it into a calculator. I didn't see any option of squaring P, maybe multiplying it with something else, or rewriting the equation into something with far less terms. One approach I thought of was to pair up each term with other terms until it equates to 1, but I don't think that is a possible solution as I don't even think every term paired up with other terms equates to 1, let alone that such a combination is unique, and that each term will be used a constant amount of times (say, we need each term ten times, then our sum is going to be 10P, which is completely fine). Can you provide us with a solution?