How do you simplify #(4sqrt5 + sqrt3)(2sqrt2 - sqrt7)#?

1 Answer
mason m
Jan 23, 2016

#8sqrt10-4sqrt35+2sqrt6-sqrt21#

Explanation:

Note that #sqrta(sqrtb)=sqrt(ab)# if #a,b>=0#.

To simplify this, we can distribute using the foil method.

#overbrace(4sqrt5(2sqrt2))^"First"+overbrace(4sqrt5(-sqrt7))^"Outside"+overbrace(sqrt3(2sqrt2))^"Inside"+overbrace(sqrt3(-sqrt7))^"Last"#

Which, using the first rule, yields

#8sqrt10-4sqrt35+2sqrt6-sqrt21#

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