I have been having trouble with this problem:
√a + √b = √3696 For all natural a and b
I tried different things but I just can't solve it
thank you for your help
It is important to notice that $\displaystyle \sqrt{3696}=4\sqrt{231}$.
Hence $\displaystyle \sqrt{a}+\sqrt{b}=4\sqrt{231}$.
From this step you can choose any combination of root a's and root b's provided they add up to $\displaystyle 4\sqrt{231}$.
I chose this combination:
$\displaystyle \sqrt{231}+3\sqrt{231}=4\sqrt{231}$
$\displaystyle \sqrt{231}+\sqrt{2079}=\sqrt{3696}$