I really stuck on this question can someone help me out and check it? What rational number, when multiplied by an irrational number, has a product that is a rational number?

a. 1/2
b. 1
c. 1/10
d. 0*****
am I right??

D is correct

thank you so much!

To determine which rational number, when multiplied by an irrational number, has a product that is rational, we need to understand the properties of irrational and rational numbers.

An irrational number is a number that cannot be expressed as a fraction of two integers and has an infinite number of non-repeating decimal places. Examples of irrational numbers include √2, π, and e.

A rational number, on the other hand, can be expressed as a fraction of two integers, where the denominator is not zero. Rational numbers can be integers, whole numbers, fractions, or terminating/repeating decimals.

In this case, we are looking for a rational number that, when multiplied by an irrational number, gives a rational product.

Let's analyze the options you provided:

a. 1/2: This is a rational number. If we multiply it by any irrational number, the product will always be rational.

b. 1: This is also a rational number. Like option a, any irrational number multiplied by 1 will result in a rational product.

c. 1/10: Another rational number. Similar to the previous options, multiplying it by an irrational number will not change the fact that the product will be rational.

d. 0: This choice is incorrect. Multiplying any number, whether it is rational or irrational, by 0 will always result in 0, which is a rational number.

Therefore, the correct answer is not listed among the options you provided. To find the rational number that, when multiplied by an irrational number, gives a rational product, you would need to look for a rational number that is the reciprocal (or multiplicative inverse) of an irrational number.