Which radical expression is an irrational number? a. ∛216 b. ∛144 c. ∛64 d. ∛125

Each cube root is the same as raising the number to the 1/3 power

The rule is

Compute each expression using a calculator

A. (216)^(1/3) = 6

B. (144)^(1/3) = 5.24 approximately

C. (64)^(1/3) = 4

D. (125)^(1/3) = 5

The only non-whole result we got was with choice B, so that is the answer. It is not possible to represent the cube root of 144 as a ratio of two whole numbers. With the other results it is possible to have a fraction of two integers. Example: 4 = 4/1, which shows that the cube root of 64 is rational.

choice B

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