Multiplying Rational and Irrational Numbers

What is a key characteristic of rational numbers?

• They can be expressed as a ratio of integers.

• They cannot be expressed as a ratio of integers.

• They always have non-repeating decimals.

• They are always negative.

When multiplying two rational numbers, what is the nature of the result?

• Always irrational

• Always rational

• Sometimes rational, sometimes irrational

• Always zero

What is the result of multiplying 3√5 by 2√3?

• 5√6, which is irrational

• 5√6, which is rational

• 6√15, which is irrational

• 6√15, which is rational

In the example of multiplying 3√2 by 4√18, what is the final result?

• 36, which is rational

• 72, which is irrational

• 72, which is rational

• 36, which is irrational

What happens when you multiply a rational number by an irrational number?

• The result can be either rational or irrational

• The result is always rational

• The result is always irrational

• The result is always zero

If you multiply 3 by 2√3, what is the nature of the result?

• Undefined

• Zero

• Irrational

• Rational

Why can't a rational number times an irrational number be rational?

• Because it contradicts the definition of irrational numbers

• Because it always results in a positive number

• Because it always results in zero

• Because it always results in a negative number