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Is 10\sqrt{10} 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 10\sqrt{10} a rational number?\newlineChoices:\newline(A) yes\newline(B) no
  1. Define 10\sqrt{10}: Step 11: Define 10\sqrt{10}.\newlineTo find if 10\sqrt{10} is rational, we first need to understand what 10\sqrt{10} means.\newline10=\sqrt{10} = the number which when multiplied by itself gives 1010.
  2. Check if 10\sqrt{10}: Step 22: Check if 10\sqrt{10} can be expressed as a fraction of two integers (ab\frac{a}{b} where aa and bb are integers and bb is not zero).\newline10\sqrt{10} is not a perfect square, meaning it cannot be expressed as a simple fraction of two integers.
  3. Determine decimal type: Step 33: Determine if 10\sqrt{10} is a terminating or repeating decimal. Since 10\sqrt{10} cannot be expressed as a fraction of two integers, it is neither a terminating nor a repeating decimal.
  4. Conclude rationality: Step 44: Conclude if 10\sqrt{10} is rational or irrational.\newlineA rational number can be expressed as a fraction of two integers. Since 10\sqrt{10} cannot be expressed this way, it is an irrational number.

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