How do you simplify #sqrt(5x^3) * sqrt(18x^4)#?

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Answer 1 · 2018-03-04T14:24:56

See a solution process below:

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

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

#sqrt(color(red)(5x^3)) * sqrt(color(blue)(18x^4)) =>#

#sqrt(color(red)(5x^3) * color(blue)(18x^4)) =>#

#sqrt(90x^7)#

Now, we can use the reverse of the rule to complete the simplification:

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

#sqrt(90x^7) =>#

#sqrt(color(red)(9x^6) * color(blue)(10x)) =>#

#sqrt(color(red)(9x^6)) * sqrt(color(blue)(10x)) =>#

#3x^3sqrt(10x)#