How do you multiply #(4sqrt5 + 3sqrt5)(2sqrt5 - 4sqrt2)#?

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Answer 1 · 2015-10-08T02:48:23

The same way you would multiply non-radicals. Break it down into simpler steps.

The front numbers multiply, then the outer, then the inner, then the last numbers. You might have learned this as "FOIL".

#= (4sqrt5 * 2sqrt5) + (4sqrt5 * -4sqrt2) + (3sqrt5 * 2sqrt5) + (3sqrt5 * -4sqrt2)#

#= (8sqrt5*sqrt5) + (-16sqrt5 * sqrt2) + (6sqrt5 * sqrt5) + (-12sqrt5 * sqrt2)#

#= 8sqrt5*sqrt5 - 16sqrt5 * sqrt2 + 6sqrt5 * sqrt5 - 12sqrt5 * sqrt2#

#= 40 - 16sqrt10 + 30 - 12sqrt10#

#= color(blue)(70 - 28sqrt10)#

Alternatively you could write this as:

#= 7(sqrt10sqrt10 - 4sqrt10)#

#= 7(2sqrt5color(green)(sqrt5) - 4sqrt2color(green)(sqrt5))#

#= color(blue)(7sqrt5(2sqrt5 - 4sqrt2))#