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!

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