Which of the following is true about the expression 2–√⋅3

Question

?(1 point)
Responses

It represents the product of two rational numbers and is equivalent to a rational number.
It represents the product of two rational numbers and is equivalent to a rational number.

It represents the product of two irrational numbers and is equivalent to an irrational number.
It represents the product of two irrational numbers and is equivalent to an irrational number.

It represents the product of one irrational and one rational number and is equivalent to an irrational number.
It represents the product of one irrational and one rational number and is equivalent to an irrational number.

It represents the product of one irrational and one rational number and is equivalent to a rational number.

Answer 1

The expression \( 2 - \sqrt{3} \) involves the rational number \( 2 \) and the irrational number \( \sqrt{3} \).

To analyze the expression:

• \( 2 \) is a rational number.
• \( \sqrt{3} \) is an irrational number.

When you subtract a rational number from an irrational number, the result is still irrational. Therefore, \( 2 - \sqrt{3} \) is an irrational number.

The appropriate statement would be:

It represents the product of one irrational and one rational number and is equivalent to an irrational number.

However, note that the given expression \( 2 - \sqrt{3} \) is not a product but rather a subtraction. If phrased as a subtraction of a product, one should be careful, but in the context of the options you provided, that describes the nature of the components correctly.