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Is the following number rational or irrational?

sqrt99
Choose 1 answer:
(A) Rational
(B) Irrational

Is the following number rational or irrational?\newline99\sqrt{99}\newlineChoose 11 answer:\newline(A) Rational\newline(B) Irrational

Full solution

Q. Is the following number rational or irrational?\newline99\sqrt{99}\newlineChoose 11 answer:\newline(A) Rational\newline(B) Irrational
  1. Evaluate 99\sqrt{99}: Evaluate whether 99\sqrt{99} can be expressed as a fraction of two integers (the definition of a rational number).99\sqrt{99} is not a perfect square, as 9999 is not the square of any integer.
  2. 99\sqrt{99} is not rational: Since 99\sqrt{99} cannot be expressed as a fraction of two integers, it is not a rational number.\newlineTherefore, 99\sqrt{99} is an irrational number.
  3. Check for simplification: Check for any possible simplification that could lead to a rational number. 9999 can be factored into 3×333 \times 33, but since 3333 is not a perfect square, the square root of 9999 cannot be simplified to a rational number.

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