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Is 3\sqrt{3} an irrational number?\newlineChoices:\newline(A) yes\newline(B) no

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Identify rational and irrational numbersright chevron icon

Full solution

Q. Is 3\sqrt{3} an irrational number?\newlineChoices:\newline(A) yes\newline(B) no
  1. Understand 3\sqrt{3}: Step 11: Understand the nature of 3\sqrt{3}.\newline3\sqrt{3} is the square root of 33, which cannot be expressed as a simple fraction of two integers.
  2. Check decimal representation: Step 22: Check if 3\sqrt{3} can be expressed as a terminating or repeating decimal.\newlineSince 3\sqrt{3} cannot be expressed as a fraction, it does not have a decimal representation that terminates or repeats.
  3. Define irrational numbers: Step 33: Define irrational numbers. An irrational number is a number that cannot be written as a simple fraction, meaning its decimal form is non-terminating and non-repeating.
  4. Compare with definition: Step 44: Compare 3\sqrt{3} with the definition of irrational numbers.\newlineSince 3\sqrt{3} is non-terminating and non-repeating, it fits the definition of an irrational number.

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