How do you simplify #\sqrt { 75a ^ { 5} b ^ { 2} }#?

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Answer 1 · 2017-10-03T12:43:48

See a solution process below:

First, rewrite the expression as:

#sqrt(25a^4b^2 * 3a)#

Now, use this rule for radicals to simplify:

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

#sqrt(color(red)(25a^4b^2) * color(blue)(3a)) =>#

#sqrt(color(red)(25a^4b^2)) * sqrt(color(blue)(3a)) =>#

#color(red)(5a^2b) * sqrt(color(blue)(3a)) =>#

#color(red)(5a^2b)sqrt(color(blue)(3a))#