How do you simplify #3sqrt15 * 5sqrt35#?

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Answer 1 · 2018-05-18T00:48:47

See a solution process below:

First, rewrite the expression as:

#3 * 5 * sqrt(15) * sqrt(35) =>#

#15 * sqrt(15) * sqrt(35)#

Next, use this rule for radicals to simplify the radicals:

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

#15 * sqrt(color(red)(15)) * sqrt(color(blue)(35)) =>#

#15 * sqrt(color(red)(15) * color(blue)(35)) =>#

#15 * sqrt(525)#

Then, rewrite the term under the radical as:

#15 * sqrt(color(red)(25) * color(blue)(21)) =>#

#15 * sqrt(color(red)(25)) * sqrt(color(blue)(21)) =>#

#15 * 5 * sqrt(color(blue)(21)) =>#

#75sqrt(21)#