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Is 7\sqrt{7} an irrational 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} an irrational number?\newlineChoices:\newline(A) yes\newline(B) no
  1. Evaluate 7\sqrt{7}: Evaluate 7\sqrt{7}.\newline7\sqrt{7} is the number that, when multiplied by itself, equals 77.\newlineThere is no whole number or simple fraction that, when squared, equals 77.
  2. Identify decimal type: Identify if 7\sqrt{7} is a terminating or non-terminating decimal.\newlineSince there is no rational number that squares to 77, 7\sqrt{7} cannot be expressed as a fraction of two integers.\newlineTherefore, 7\sqrt{7} is a non-terminating decimal.
  3. Determine irrationality: Determine if 7\sqrt{7} is an irrational number. A number that is non-terminating and non-repeating is considered irrational. Since 7\sqrt{7} is non-terminating and cannot be expressed as a fraction, it is irrational.

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