7root3/(10^1/2 +3^1/2) - 2root5/(6^1/2+5^1/2) - 3root2/(15^1/2+3^root2)

do you really mean 3^√2 ?

If the other "root" items are cube root, 5th root, and square root, and all those x^1/2 items are other square roots, man I don't see much of anything that can be done to simplify things

7∛(√10 + √3)

doesn't give me any ideas.