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Which of these numbers is NOT irrational?

Class 9Number SystemsNumber Systems
  • A
  • B
  • C
  • Dπ − 2

Step-by-Step Solution

, a terminating decimal and therefore rational — a root sign does not automatically mean irrational. is irrational, and rational ± irrational stays irrational, so and π − 2 are irrational too.
Answer: A)

Key idea: Working with irrationals

**Sum/difference of two irrationals can be rational.** Example: .
**Product of two irrationals can be rational.** Example: .
**Sum of a rational and an irrational is always irrational.** is irrational.
**Product of a non-zero rational and an irrational is always irrational.** is irrational.

These facts let you build new irrationals and prove things irrational by contradiction.

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