Question

please label which of these are rational, and which are irrational.
3.5 x 4.3
2π + 7
√3 + 2/5
0.5
√2
2/3 + √5
0.5 + 3/4
√49
7/π

Answer 1

- 3.5 × 4.3 — Rational. (3.5 = 7/2 and 4.3 = 43/10, product = 15.05 = 301/20.)
- 2π + 7 — Irrational. (π is irrational; rational + irrational is irrational.)
- √3 + 2/5 — Irrational. (√3 is irrational; adding a rational leaves it irrational.)
- 0.5 — Rational. (0.5 = 1/2.)
- √2 — Irrational.
- 2/3 + √5 — Irrational. (√5 is irrational; adding a rational yields an irrational.)
- 0.5 + 3/4 — Rational. (0.5 + 0.75 = 1.25 = 5/4.)
- √49 — Rational. (√49 = 7.)
- 7/π — Irrational. (If 7/π were rational, π would be rational; contradiction.)