How do you simplify #3/root(3) (24)# ?

1 Answer
Dahlia S.
Mar 10, 2018

#root 3(9)/2#

Explanation:

First you can start by simplifying #root 3 24#. 24 can be rewritten as #3*8#, and we can use that to simplify.

#root 3 (3*8) = root 3 (3*2^3)=root 3 (2^3)*root 3 (3)=2root3(3)#.

We have now simplified the expression to #3/(2root3(3))#, but we're not done yet. In order to fully simplify an expression, you must remove all radicals from the denominator. To do that, we will multiply both the numerator and denominator by #root3(3)# twice.

#3/(2root3(3))*root3(3)/root3(3)*root3(3)/root3(3)=(3*(root3(3))^2)/(2(root3(3))^3)=(3*root3(3^2))/(2*3)=root3(9)/2# .

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