Question

When proving that the sum of two rational numbers is rational in the expression a+c/bd
, which value could be used for a in order to apply the proof?(1 point)
Responses

π
pi

3
3

3–√
Start Root 3 End Root

3/0

Answer 1

To prove that the sum of two rational numbers is rational, we need to use values for \( a \) and \( c \) that are rational. A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

Let's evaluate the options given:

1. **π**: This is an irrational number.
2. **3**: This is a rational number (it can be expressed as \( \frac{3}{1} \)).
3. **\( 3-\sqrt{3} \)**: \( \sqrt{3} \) is irrational, so \( 3 - \sqrt{3} \) is also irrational.
4. **\( \frac{3}{0} \)**: This expression is undefined since division by zero is not allowed.

The only rational option among these is **3**. Therefore, you can use **3** for \( a \) in order to apply the proof that the sum of two rational numbers is rational.