Calling the sum of the two square roots ‘S’, and the difference of the two square roots ‘D’, the expression becomes S*sqrt(D/S)

We notice that S*D is a difference of two squares and is therefore equal to 2024-2023, which is 1.

If we take the fraction under the square root, we can multiply top and bottom by D without changing its value. The top becomes D^2 and the bottom becomes 1. Then the square root of a square means that the whole square root expression can be replaced with D. Then the entire expression is just S*D, which of course is just 1.

The numbers 2024 and 2023 in this puzzle are unimportant; what’s important is that the first is one more than the second.