Question
does √3 +2/4 have a rational sum?
Answers
GPT-4o mini
To determine whether the sum \( \sqrt{3} + \frac{2}{4} \) has a rational value, let's break it down:
1. Simplify \( \frac{2}{4} \):
\[
\frac{2}{4} = \frac{1}{2}
\]
2. Now rewrite the expression:
\[
\sqrt{3} + \frac{1}{2}
\]
3. We know that \( \sqrt{3} \) is an irrational number. A rational number plus an irrational number is always irrational.
Therefore, the sum \( \sqrt{3} + \frac{1}{2} \) is irrational. Thus, \( \sqrt{3} + \frac{2}{4} \) does NOT have a rational sum.
1. Simplify \( \frac{2}{4} \):
\[
\frac{2}{4} = \frac{1}{2}
\]
2. Now rewrite the expression:
\[
\sqrt{3} + \frac{1}{2}
\]
3. We know that \( \sqrt{3} \) is an irrational number. A rational number plus an irrational number is always irrational.
Therefore, the sum \( \sqrt{3} + \frac{1}{2} \) is irrational. Thus, \( \sqrt{3} + \frac{2}{4} \) does NOT have a rational sum.