How do you simplify #sqrt12*sqrt15#?

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Answer 1 · 2018-03-05T03:40:23

See a solution process below:

First, use this rule for radicals to rewrite the expression as:

#sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))#

#sqrt(color(red)(12)) * sqrt(color(blue)(15)) => sqrt(color(red)(12) * color(blue)(15)) => sqrt(180)#

Next, rewrite the expression as:

#sqrt(180) => sqrt(36 * 5)#

Now, use the rule above in reverse to complete the simplification:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#sqrt(color(red)(36) * color(blue)(5)) => sqrt(color(red)(36)) * sqrt(color(blue)(5)) => 6sqrt(5)#