How do you simplify #\frac { 8} { \root[ 3] { 6} } #?

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Answer 1 · 2017-11-08T19:55:56

#8/root(3)(6) = 4/3root(3)(36)#

Given:

#8/root(3)(6)#

Note the prime factorisation of #6#:

#6 = 2*3#

has no square, let alone cube factors.

So #root(3)(6)# has no simpler form, and in order to rationalise it we need to multiply by #root(3)(6)^2 = root(3)(6^2) = root(3)(36)#

So:

#8/root(3)(6) = (8root(3)(36))/(root(3)(6)root(3)(36)) = 8/6root(3)(36) = 4/3root(3)(36)#