How do you simplify #3root4(24)*5root4(2)#?

1 Answer
Jun 11, 2017

Answer:

See a solution process below:

Explanation:

First, rewrite this expression as:

#(3 * 5)(root(4)(24) * root(4)(2)) => 15(root(4)(24) * root(4)(2))#

Next use this rule for radicals to combine the radicals:

#root(n)(color(red)(a)) * root(n)(color(blue)(b)) = root(n)(color(red)(a) * color(blue)(b))#

#15(root(4)(color(red)(24)) * root(4)(color(blue)(2))) => 15root(4)(color(red)(24) * color(blue)(2)) => 5root(4)(48)#

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

#5root(4)(48) => 15root(4)(color(red)(16) * color(blue)(3)) => 15(root(4)(color(red)(16)) * root(4)(color(blue)(3))) => 15 * 2 * root(4)(3) =>#

#30root(4)(3)#