How do you simplify # ""^5sqrt(96)#

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Answer 1 · 2014-10-25T16:22:16

#root 5 96#

#=> root 5 (2^5*3)#

#=> root 5 (2^5) * root 5 3#

#=> 2root 5 3#

Answer 2 · 2014-10-25T16:25:57

Since #96=2^5cdot3#,

#root[5]{96}=root[5]{2^5cdot3}#

by distributing the 5th-root,

#=root[5]{2^5}cdot root[5]{3}#

by cancelling out the 5th-power and the 5th-root,

#=2 root[5]{3}#.

I hope that this was helpful.