How do you simplify #64^(1/4)#?

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Answer 1 · 2016-06-19T10:28:25

#2sqrt2#

#64=2^6#
So it can be written as
#(2^6)^(1/4)#
=#2^(3/2)=2sqrt2#

Answer 2 · 2016-06-19T11:14:40

#2sqrt2#

One should remember that finding a fourth root is the same as finding the square root twice.

#root(4)x =sqrt(sqrtx)#

#root(4)64 = sqrt(sqrt64) = sqrt8#

However 8 is not a perfect square so it does not have an exact square root.

#sqrt8 = sqrt(4 xx 2) = 2sqrt2#