How do you simplify (5 square root 2 + square root 3)(square root 2 + 2 square root 3)?

1 Answer
Jul 27, 2015

Answer:

#=color(blue)(16 +11sqrt(6)#

Explanation:

Expressing the question in numbers:

#=color(blue)((5sqrt2+sqrt3)) * (sqrt2+2sqrt3)#

Each term within the first bracket needs to be multiplied with each term within the second bracket.

#=color(blue)((5sqrt2)) * (sqrt2+2sqrt3)+color(blue)((sqrt3)) *(sqrt2+2sqrt3)#

#=[(5sqrt2) (sqrt2) + (5sqrt2) (2sqrt3)]+[(sqrt3)(sqrt2) + (sqrt3)*(2sqrt3)]#

#=[5*2 +10sqrt(2*3)] + [sqrt6+2*3]#

#=[10 +10sqrt(6)] + [sqrt6+6]#

Grouping like terms

#=16 +11sqrt(6)#