Question

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

Answer 1

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)