How do you simplify #(root3(10))/(root3(32))#?

1 Answer
Aug 24, 2017

Answer:

See a solution process below:

Explanation:

First, we can rewrite the expression as:

#root(3)(10)/root(3)(8 * 4) => root(3)(10)/(root(3)(8)root(3)(4)) => root(3)(10)/(2root(3)(4))#

Next, we can rationalize the fraction by multiplying by the appropriate form of #1#:

#root(3)(2)/root(3)(2) xx root(3)(10)/(2root(3)(4)) =>#

#(root(3)(2)xx root(3)(10))/(2root(3)(4) xx root(3)(2)) =>#

#root(3)(2 xx 10)/(2root(3)(4 xx 2)) =>#

#root(3)(20)/(2root(3)(8)) =>#

#root(3)(20)/(2 xx 2)#

#root(3)(20)/4#