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

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Answer 1 · 2015-07-27T05:33:29

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

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

$=16 +11sqrt(6)$