Question
Sums and products of rational and irrational numbers practice what type of numbers will result from the sum of a rational number and a irrational number one irrational to rational 30 4 equal
Answers
GPT-4o mini
When you add a rational number to an irrational number, the result is always an irrational number.
For example:
1. Let's say you have a rational number, like \( 30 \) (which can be expressed as \( \frac{30}{1} \)), and an irrational number, like \( \sqrt{2} \).
2. If you add them together:
\[
30 + \sqrt{2}
\]
The result \( 30 + \sqrt{2} \) is irrational.
So if you add any rational number to an irrational number, the result will be irrational.
### Summary:
- **Rational + Irrational = Irrational**
Thus, for your question, if you have \( 30 \) (rational) and \( 4 \) (which is also rational) and are adding any irrational number to either one of them, the sum will still remain irrational when involving at least one irrational number.
For example:
1. Let's say you have a rational number, like \( 30 \) (which can be expressed as \( \frac{30}{1} \)), and an irrational number, like \( \sqrt{2} \).
2. If you add them together:
\[
30 + \sqrt{2}
\]
The result \( 30 + \sqrt{2} \) is irrational.
So if you add any rational number to an irrational number, the result will be irrational.
### Summary:
- **Rational + Irrational = Irrational**
Thus, for your question, if you have \( 30 \) (rational) and \( 4 \) (which is also rational) and are adding any irrational number to either one of them, the sum will still remain irrational when involving at least one irrational number.