Question

Which radical expression is an irrational number?

A. ∛216
B. ∛144
C. ∛64
D. ∛125

Answer 1

Option B

Explanation:

∛216 = 6

∛144 = 5.241482788........ This goes on without bounds. Try it on your calculator.

Its this one

C is 4 and D is 5.

Answer 2

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

The rule is
`\sqrt[n]{x} = x^(1/n)`

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.

Answer: choice B