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Consider the statement: 'If is irrational, then a is irrational.'
Which choice correctly judges this for a real number a?

Class 10Irrational NumbersNumber Systems
  • ATrue, because a rational squared is rational
  • BFalse, 2 is a counterexample
  • CTrue only for integers
  • DFalse, is a counterexample

Step-by-Step Solution

If a were rational, would be rational. Since is irrational, a cannot be rational; hence a is irrational. The statement is true.
Answer: A) True, because a rational squared is rational

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