What is radical form for #4^(1/3)#?

1 Answer
Acquaintance
Jun 12, 2016

#root(3) 4#

Explanation:

We can write #4^(1/3)# in radical form, but not with square roots. We can write this using cube roots.

Here is a quick differentiation:

#sqrt64 = 8 or -8#
#root(3)64 = 4#

So, if we multiply #8# or #-8# by itself, we get 64. If we multiply 4 by itself three times, we get 64. This same theory works with fraction exponents that get smaller (#x^(1/4), x^(1/5), x^(1/6)#).

Anything written to the #1/3# power is the cube root of that base number.

Given this, we can write:

#4^(1/3)# = #root(3)4#

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