How do you simplify #(2\sqrt { 6} ) ^ { 3}#?

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Answer 1 · 2018-03-25T09:11:13

#color(blue)((2\sqrt { 6} ) ^ { 3} = 48sqrt(6)#

Given the radical expression:

#(2\sqrt { 6} ) ^ { 3}#

#rArr 2^3*(sqrt(6))^3#

#rArr 2^3*(6^(1/2))^3#

#rArr 2^3*(6)^(3/2)#

As, #3/2 =1+1/2#

#rArr 2^3*6^1*6^(1/2)#

#rArr 2^3*6sqrt(6)#

#rArr 2^3*(2*3)*sqrt(6#

#rArr 2^3*2^1*3*sqrt(6)#

#rArr 2^4*3*sqrt(6)#

#rArr 48sqrt(6)#

Hence,

#color(blue)((2\sqrt { 6} ) ^ { 3} = 48sqrt(6)#