We essentially have the following
color(blue)(5)color(lime)(sqrt3)*color(blue)(6)color(lime)(sqrt10)-color(blue)(5)color(lime)(sqrt3)*color(blue)(6)color(lime)(sqrt3)5√3⋅6√10−5√3⋅6√3
Which can be simplified if we multiply the integers and square roots together, respectively. We'll get
color(blue)((5*6))color(lime)(sqrt3sqrt10)-color(blue)((5*6))color(lime)(sqrt3sqrt3)(5⋅6)√3√10−(5⋅6)√3√3
Which simplifies to
color(blue)(30)color(lime)(sqrt30)-color(blue)(30)*color(lime)(3)30√30−30⋅3
=>color(blue)(30)color(lime)(sqrt30)-90⇒30√30−90
Since 3030 has no perfect square factors, we cannot simplify the radical any further. We can factor a 3030 out of both terms, however. We get
30(sqrt30-3)30(√30−3)
Hope this helps!
