How do you simplify #(2sqrt7+ sqrt3)(3sqrt7 + √2)#?

1 Answer
Oct 13, 2017

Answer:

#14+2sqrt14+3sqrt21+sqrt6#

Explanation:

#(color(red)(2sqrt7)+color(green)(sqrt3))(color(blue)(3sqrt7)+color(orange)(sqrt2))#

Multiply every term in the first brackets to every term in the second bracket.

#=color(red)(2sqrt7)*color(blue)(3sqrt7)+color(red)(2sqrt7)color(orange)(sqrt2)+color(blue)(3sqrt7)color(green)(sqrt3)+color(orange)(sqrt2)color(green)(sqrt3)#

#=6times7+2sqrt(7times2)+3sqrt(7times3)+sqrt(2times3)#

#=42+2sqrt14+3sqrt21+sqrt6#

As there are no like terms, this is the final answer #uarr#.