How do you simplify (square root 5 + 9 square root 2)(4 square root 5 - square root 2)?

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Answer 1 · 2015-07-27T11:40:11

$=color(blue)(2 +35sqrt(10)$

Expressing the question in numbers:

$=color(blue)((sqrt5+9sqrt2)) * (4sqrt5 - sqrt2)$

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

$=color(blue)((sqrt5)) * (4sqrt5 - sqrt2)+color(blue)((9sqrt2)) *(4sqrt5 - sqrt2)$

$=[(sqrt5) (4sqrt5) + (sqrt5)(-sqrt2)]+[9(sqrt2)(4sqrt5) + (9sqrt2)*(-sqrt2)]$

$=[4*5 -sqrt(2*5)] + [36sqrt(2*5) -18]$

$=[20 -sqrt(10)] + [36sqrt10-18]$

Grouping like terms
$=(20-18) -sqrt10+36sqrt10$

$=2 +35sqrt(10)$