How do you simplify #5sqrt3(6sqrt10-6sqrt3)#?

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Answer 1 · 2018-06-21T22:47:06

#30(sqrt30-3)#

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)#

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)#

Which simplifies to

#color(blue)(30)color(lime)(sqrt30)-color(blue)(30)*color(lime)(3)#

#=>color(blue)(30)color(lime)(sqrt30)-90#

Since #30# has no perfect square factors, we cannot simplify the radical any further. We can factor a #30# out of both terms, however. We get

#30(sqrt30-3)#

Hope this helps!