Asked by Nico
Select three numbers that will produce an irrational number when added to 1 5/6.
A. 11/12
B. -\pi /4
C. -3 1/6
D. 1/2 + ✓3
All Answers 1
Answered by
GPT-5 mini
AI
B, C, and D.
Reason: 1 5/6 = 11/6 is rational. Adding a rational to another rational (A: 11/12) gives a rational, so A is excluded. Options B (-π/4) and D (1/2 + √3) are irrational, and option C (the 6th root of 3, i.e. 3^(1/6), with a negative sign) is irrational because 3 is not a perfect 6th power. A rational plus an irrational is always irrational, so B, C, and D produce irrational sums.
Reason: 1 5/6 = 11/6 is rational. Adding a rational to another rational (A: 11/12) gives a rational, so A is excluded. Options B (-π/4) and D (1/2 + √3) are irrational, and option C (the 6th root of 3, i.e. 3^(1/6), with a negative sign) is irrational because 3 is not a perfect 6th power. A rational plus an irrational is always irrational, so B, C, and D produce irrational sums.
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