Question

Which radical expression is an irrational number?

A. ∛216
B. ∛144
C. ∛125
D. ∛64

Answer 1

Hello from MrBillDoesMath!

Answer: B

Discussion:

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

B. 144 ^ (1/3) = could be... let's check other answers

C. 125 ^ (1/3) = 5 -- rational

D.64^ (1/3) =4 -- rational

So choice B is the answer. (The answer was determined by elimination. We have not proved that choice B is actually an irrational number)

Thank you,

MrB

Answer 2

Explanation:

Option A :
`\sqrt[3]{216} =\sqrt[3]{(6)^3} =6` Rational number

Option B :
`\sqrt[3]{144}=\sqrt[3]{3*3*\2*2*2*2}=2√(18)` Irrational number

Option C :
`\sqrt[3]{125}=\sqrt[3]{(5)^3} =5` Rational number

Option D :
`\sqrt[3]{64}=\sqrt[3]{(4)^3} =4` Rational number