Question

Which of the following is irrational?(1 point)
Responses

3.6363636363636363...
3.6363636363636363...

3√4

Start Fraction Start Root 3 End Root over 4 End Fraction

52.781654292
52.781654292

−7837

negative 7 Start Fraction 8 over 37 End Fraction

Answer 1

Irrational among those choices: ∛4 (the cube root of 4) and (√3)/4.

Reason:
- ∛4 is irrational because 4 = 2^2 is not a perfect cube (the exponent of the prime 2 is 2, not divisible by 3), so its cube root cannot be a rational number.
- √3 is irrational, and dividing it by the nonzero rational 4 gives (√3)/4, which is also irrational.

The others are rational:
- 3.636363... = 40/11 (repeating decimal),
- 52.781654292 is a terminating decimal (rational),
- −7837 is an integer (rational),
- −7 8/37 is a rational mixed number.