Real Number Arithmetic and Square Roots

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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?

$b^2 = a$ and $b > 0$ Signup and view all the answers

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

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

Which statement is true about irrational numbers?

Every irrational number is a real number. 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?

At point O 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?

Rational number Signup and view all the answers

Are all square roots of positive integers irrational?

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

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

Natural number Signup and view all the answers

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

Always results in an irrational number Signup and view all the answers

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

Irrational Signup and view all the answers

Which of the following numbers is considered irrational?

3 Signup and view all the answers

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

Could be rational or irrational Signup and view all the answers

When multiplying two irrational numbers, the result is:

Could be rational or irrational Signup and view all the answers

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

An irrational number Signup and view all the answers

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

An irrational number Signup and view all the answers

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

No numbers remain Signup and view all the answers