Real Number Arithmetic and Square Roots
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Questions and Answers

What is the expected result when adding a rational number and an irrational number?

  • The result can be rational or irrational (correct)
  • The result is always rational
  • The result is always an integer
  • The result is always irrational
  • Which of the following statements is true when multiplying a non-zero rational number with an irrational number?

  • The result is always irrational (correct)
  • The result is always rational
  • The result can be rational or irrational
  • The result is always an integer
  • If you add or subtract two irrational numbers, what may the result be?

  • Always an integer
  • Always rational
  • Either rational or irrational (correct)
  • Always irrational
  • What does it mean when $a = b$ for real numbers?

    <p>$b^2 = a$ and $b &gt; 0$</p> Signup and view all the answers

    How does one represent $n$ on the number line for any positive integer $n$?

    <p>By representing a point at distance $n$ from a fixed point</p> Signup and view all the answers

    Which statement is true about irrational numbers?

    <p>Every irrational number is a real number.</p> Signup and view all the answers

    In the process of finding $x$ for any given positive real number $x$, how should the midpoint of $AC$ be marked?

    <p>At point O</p> Signup and view all the answers

    If a point is represented as $m$, where $m$ is a natural number, what type of number does it represent?

    <p>Rational number</p> Signup and view all the answers

    Are all square roots of positive integers irrational?

    <p>No, some square roots of positive integers are rational.</p> Signup and view all the answers

    What type of number can be created by following the process described in the 'square root spiral' activity?

    <p>Natural number</p> Signup and view all the answers

    What happens when you divide an irrational number by another irrational number?

    <p>Always results in an irrational number</p> Signup and view all the answers

    When multiplying two irrational numbers, the result is most likely to be:

    <p>Irrational</p> Signup and view all the answers

    Which of the following numbers is considered irrational?

    <p>3</p> Signup and view all the answers

    If we add an irrational number to a rational number, the result is:

    <p>Could be rational or irrational</p> Signup and view all the answers

    When multiplying two irrational numbers, the result is:

    <p>Could be rational or irrational</p> Signup and view all the answers

    Dividing an irrational number by a rational number can result in:

    <p>An irrational number</p> Signup and view all the answers

    Taking the square root of an irrational number may result in:

    <p>An irrational number</p> Signup and view all the answers

    If all irrational numbers are put into a bag with rational numbers, what remains on the number line?

    <p>No numbers remain</p> Signup and view all the answers

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