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5 January, 11:55

Select from the drop-down menus to correctly complete the proof.

To prove that 3√5 is irrational, assume the product is rational and set it equal to a/b, where b is not equal to 0. Isolating the radical gives √5 = a/3b (All one fraction). The right side of the equation is [Rational or Irational]. Because the left side of the equation is [Rational or Irational], this is a contradiction. Therefore, the assumption is wrong, and the number is [Rational or Irational].

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Answers (2)
  1. 5 January, 12:15
    0
    Rational; irrational; irrational.

    Step-by-step explanation:

    a/3b is a rational number, as it is represented by a fraction and b ≠ 0. This means the first blank is "rational."

    √5 is an irrational number. This means the second blank is "irrational."

    Since we have an irrational number set equal to a rational number, this is a contradiction. This means our original assumption is wrong, and the number is irrational. This is the third blank.
  2. 5 January, 12:24
    0
    1. rational

    2. irrational

    3. irrational
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