How can you write the expression with rationalized denominator? (^3 sqrt 2)/(^3 sqrt 6)

Question

(^3 sqrt 9)/3
(2 + ^3 sqrt 9)/6
(^3 sqrt 9)/6
(^3 sqrt 72)/3

Answer 1

To rationalize the denominator of the expression (^3 sqrt 2)/(^3 sqrt 6), you can multiply both the numerator and denominator by (^3 sqrt 6):

= (^3 sqrt 2)(^3 sqrt 6) / (^3 sqrt 6)(^3 sqrt 6)
= ^3 sqrt 12 / 6
= ^3 sqrt 4 * ^3 sqrt 3 / 6
= 2 * ^3 sqrt 3 / 6
= (^3 sqrt 3) / 3

Therefore, the expression with a rationalized denominator is (^3 sqrt 3) / 3.