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Which of these surds is NOT yet in simplest form?

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

Step-by-Step Solution

20 = contains the perfect square 4, so . The numbers 7, 2 and 15 have no perfect-square factor other than 1, so those three are already simplest.
Answer: B)

Key idea: Decimal expansion test

**Rational ↔ terminating OR non-terminating recurring decimal.**
**Irrational ↔ non-terminating non-recurring decimal.**

Example: (terminating → rational).
Example: … (recurring → rational).
Example: … (non-terminating non-recurring → irrational).

**When does terminate?** Exactly when the denominator (in simplest form) has only 2's and 5's as prime factors. So terminates: 0.125. But doesn't: 0.1666…

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