How do you simplify #(3sqrt11+3sqrt15)(3sqrt3-2sqrt2)#?

1 Answer
Apr 26, 2017

Answer:

#9sqrt33-6sqrt22+27sqrt5-6sqrt30#

Explanation:

#(color(red)(3sqrt11color(green)(+3sqrt15)))(color(blue)(3sqrt3)color(brown)(-2sqrt2))#

Multiply each term in the bracket with each other term in the other bracket

#color(red)(3sqrt11)(color(blue)(3sqrt3))+color(red)(3sqrt11)(color(brown)(-2sqrt2))+color(green)(3sqrt15)(color(blue)(3sqrt3))+color(green)(3sqrt15)(color(brown)(-2sqrt2))#

Multiply the whole number with the whole number and the square root with the square root

#color(red)3*color(blue)3sqrt(color(red)11*color(blue)3)+color(red)3*color(brown)(-2)sqrt(color(red)11*color(brown)2)+color(green)3*color(blue)3sqrt(color(green)15*color(blue)3)+color(green)3*color(brown)(-2)sqrt(color(green)15*color(brown)2)#

#9sqrt33-6sqrt22+9sqrt45-6sqrt30#

#9sqrt45# can be simplified

#9sqrt45=9*sqrt(3*3*5)=9*sqrt(3^2*5)=9*sqrt(3^2)*sqrt5=9*3sqrt5=27sqrt5#

So #9sqrt33-6sqrt22+color(magenta)(9sqrt45)-6sqrt30# can be rewritten as

#9sqrt33-6sqrt22+color(magenta)(27sqrt5)-6sqrt30#

These numbers can't be combined due to different numbers inside the roots, so this is the final answer.