How do you simplify #root3(16) +root3(54) #?

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Answer 1 · 2017-06-12T02:23:58

See a solution process below:

First, rewrite the expression by rewriting each radical using this rule for radicals:

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

#root(3)(16) + root(3)(54) => root(3)(color(red)(8) * color(blue)(2)) + root(3)(color(red)(27) * color(blue)(2)) =>#

#(root(3)(color(red)(8)) * root(3)(color(blue)(2))) + (root(3)(color(red)(27)) * root(3)color(blue)(2)) =>#

#2root(3)(color(blue)(2)) + 3root(3)color(blue)(2)#

We can factor and combine:

#(2 + 3)root(3)color(blue)(2) =>#

#5root(3)color(blue)(2)#