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Difficulty: 1/102023 NMTC 2023 (QII-38)

Which of the following real numbers is NOT irrational (i.e., is rational)?

Options:

  • B.

  • C.

  • D.

Guide / Hint

Hint 1: Understand that a number is rational (not irrational) if it simplifies to an integer or a simple fraction.

Hint 2: Simplify the square root of 4.

Hint 3: Since , which is an integer, it is rational. This is at option index 0.

Solution

Step 1 (Define rational and irrational):

  • A real number is rational if it can be written in the form where and are integers and .

  • A real number is irrational if it cannot be written in that form.

Step 2 (Analyze the square roots):

  • are square roots of prime numbers (which are not perfect squares). They are well-known to be irrational numbers.

  • is the square root of a perfect square ():

Since , it is a rational number, meaning it is NOT irrational.

Step 3 (Conclusion): The number is rational, so it is not irrational. This corresponds to option index 0.

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