How do you multiply $(3sqrt6)(2sqrt50)$ ?

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Answer 1 · 2015-12-21T16:58:09

$=color(blue)(60sqrt3$

$color(blue)(3sqrt6) xx 2sqrt50$

$= color(blue)(3 xx2) xx sqrt6 xx sqrt50$

$= color(blue)(6) xx sqrt300$

Prime factorising $300$

$300=2*2*5*5*3$

So, $sqrt300=sqrt(2*2*5*5*3)$

$=sqrt(2^2xx5^2xx3)$

$=2 xx 5sqrt( 3)$

$=10sqrt( 3)$

The expression becomes:
$= color(blue)(6) xx sqrt300 = color(blue)(6 xx 10sqrt3$

$=color(blue)(60sqrt3$

How do you multiply (3sqrt6)(2sqrt50) (3sqrt6)(2sqrt50)?