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 $b &gt; 0$ (D)</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 (A)</p> Signup and view all the answers

Which statement is true about irrational numbers?

<p>Every irrational number is a real number. (B)</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 (B)</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 (B)</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. (B)</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 (A)</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 (C)</p> Signup and view all the answers

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

<p>Irrational (A)</p> Signup and view all the answers

Which of the following numbers is considered irrational?

<p>3 (B)</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 (B)</p> Signup and view all the answers

When multiplying two irrational numbers, the result is:

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

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

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

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

<p>An irrational number (A)</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 (C)</p> Signup and view all the answers

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