Answer:
10√13 +25√2
Step-by-step explanation:
Factoring the given radicals to primes gives us a clue as to how to simplify the expression.
[tex]\sqrt{1300}-\sqrt{882}+\sqrt{968}+\sqrt{1152}\\\\=\sqrt{10^2\cdot13}-\sqrt{21^2\cdot2}+\sqrt{22^2\cdot2}+\sqrt{24^2\cdot2}\\\\=10\sqrt{13}+(-21+22+24)\sqrt{2}=\boxed{10\sqrt{13}+25\sqrt{2}}[/tex]
