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Is 7\sqrt{7} a rational number?\newlineChoices:\newline(A) yes\newline(B) no

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Identify rational and irrational square rootsright chevron icon

Full solution

Q. Is 7\sqrt{7} a rational number?\newlineChoices:\newline(A) yes\newline(B) no
  1. Understand rational number definition: Step 11: Understand the definition of a rational number.\newlineA rational number can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero.
  2. Evaluate 7\sqrt{7}: Step 22: Evaluate 7\sqrt{7}.\newline7\sqrt{7} is the number that when multiplied by itself gives 77.\newlineThere is no integer whose square is 77, indicating that 7\sqrt{7} cannot be expressed as a fraction of two integers.
  3. Determine decimal type: Step 33: Determine if 7\sqrt{7} is a terminating or repeating decimal. Since 7\sqrt{7} cannot be expressed as a fraction of two integers, it is neither a terminating nor a repeating decimal. It is a non-terminating, non-repeating decimal.
  4. Conclude 7\sqrt{7} type: Step 44: Conclude if 7\sqrt{7} is rational or irrational.\newlineSince 7\sqrt{7} is a non-terminating, non-repeating decimal and cannot be expressed as a fraction of two integers, it is an irrational number.

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