Question

let us write what should be added with √5+√3 to get the sum 2√5

Answer 1

√5-√3 should be added

Answer 2

let us assume that x should be added to
$\sqrt{5} + \sqrt{3} + x = 2 \sqrt{5}$
We know
$2 \sqrt{5}$
is
$\sqrt{5 } + \sqrt{5} = 2 \sqrt{5}$
Now putting in formula
$\sqrt{5} + \sqrt{3} + x = \sqrt{5} + \sqrt{5}$
So
$\sqrt{3 } + x = \sqrt{5} \\ x = \sqrt{5} - \sqrt{3}$