Question

write an equivalent expression without a perfect square or perfect cub factor other than 1 in the radicand.
cubed root of 108

Write an expression for each product or quotient without a perfect square or perfect cube factor other than 1 in the radicand.
square root of 14 times square root of 21

Make sure to write it in the Simplest form

Answer 1

1) cube root(108)

108 = 2^2 · 3^3, so cube root(108) = 3 · cube root(4).
(cube root radicand 4 has no perfect cube factor > 1)

2) sqrt(14) · sqrt(21)

sqrt(14·21) = sqrt(294) and 294 = 2·3·7^2, so sqrt(294) = 7·sqrt(6).
(the radicand 6 has no perfect square factor > 1)