What is the radical part of both ^3 square root 54 and ^3 square root 128 when the expressions are simplified?

The radical parts of the two expressions above will be as follows;

a]

^3 sqrt 54 = (54) ^ (1/3)

= (2*27) ^ (1/3)

= (2) ^ (1/3) * (27) ^ (1/3)

= (2) ^ (1/3) * (3³) ^ (1/3)

=3 (2) ^ (1/3)

or

3 (^3√2)

Hence the answer is 3 (2) ^ (1/3) = 3 (^3√2)

a] ^3sqrt 128 = (128) ^ (1/3)

= (2*64) ^ (1/3)

=2^ (1/3) * 64^ (1/3)

=2^ (1/3) * (4³) ^ (1/3)

=2^ (1/3) * 4^ (3*1/3)

=2^ (1/3) * 4

=4 (2) ^ (1/3)

=4 (^3√2)