How do you simplify #(2sqrt5 - 4sqrt6) (3sqrt3 + 8sqrt2)#?

1 Answer
Mar 5, 2018

Answer:

#(2sqrt5-4sqrt6)(3sqrt3+8sqrt2)=6sqrt15+16sqrt10-36sqrt2-64sqrt3)#

Explanation:

#(2sqrt5-4sqrt6)(3sqrt3+8sqrt2)#

Expand using the FOIL method.

https://formulas.tutorvista.com/math/foil-formula.html

#(2sqrt5-4sqrt6)(3sqrt3+8sqrt2)=#

#color(blue)((2sqrt5*3sqrt3))+color(teal)((2sqrt5*8sqrt2))+color(red)((-4sqrt6*3sqrt3))+color(green)((-4sqrt6*8sqrt2)#

Multiply integers and square roots.

#color(blue)((2*3*sqrt5sqrt3))+color(teal)((2*8*sqrt5sqrt2))+color(red)((-4*3*sqrt6sqrt3))+color(green)((-4*8*sqrt6sqrt2))#

Simplify.

#color(blue)((6sqrt15))+color(teal)((16sqrt10))+color(red)((-12sqrt18))+color(green)((-32sqrt12))#

The first two sets of parentheses are cannot be simplified further. The second two sets of parentheses need further simplification.

Prime factorize #color(red)((-12sqrt18))#.

#color(blue)((6sqrt15))+color(teal)((16sqrt10))+color(red)((-12sqrt(2*3*3))+color(green)((-32sqrt12)#

Simplify.

#color(blue)((6sqrt15))+color(teal)((16sqrt10))+color(red)((-12*3sqrt2))+color(green)((-32sqrt12))#

Simplify.

#color(blue)((6sqrt15))+color(teal)((16sqrt10))+color(red)((-36sqrt2))+color(green)((-32sqrt12))#

Prime factorize #color(green)((-32sqrt12))#.

#color(blue)((6sqrt15))+color(teal)((16sqrt10))+color(red)((-36sqrt2))+color(green)((-32sqrt(2*2*3)))#

Simplify.

#color(blue)((6sqrt15))+color(teal)((16sqrt10))+color(red)((-36sqrt2))+color(green)((-32*2sqrt3))#

Simplify.

#color(blue)((6sqrt15))+color(teal)((16sqrt10))+color(red)((-36sqrt2))+color(green)((-64sqrt3))#

Simplify.

#6sqrt15+16sqrt10-36sqrt2-64sqrt3#