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Which of these expressions has an IRRATIONAL value?

Class 9Number SystemsNumber Systems
  • A
  • B
  • C
  • D

Step-by-Step Solution

— a non-zero rational times an irrational, so irrational. The others all collapse to rationals: , 6 (the surds cancel), and .
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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