How do you simplify #\(2\sqrt { 15} )( 3\sqrt { 30})#?

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Answer 1 · 2017-09-19T03:38:02

See a solution process below:

Rewrite the expression as:

#(2 * 3)(sqrt(15)sqrt(30)) => 6sqrt(15)sqrt(30)#

Now, rewrite the the radicals using this rule of radicals:

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

#6sqrt(color(red)(15))sqrt(color(blue)(30)) =>#

#6sqrt(color(red)(15) * color(blue)(30)) =>#

#6sqrt(450)#

We can now rewrite this as:

#6sqrt(450) =>#

#6sqrt(color(red)(225) * color(blue)(2)) =>#

#6sqrt(color(red)(225))sqrt(color(blue)(2)) =>#

#6 * 15sqrt(2) =>#

#90sqrt(2)#