Question
which of the following is ratinoal?
3−−√ + 3−−√
3−−√ x 3−−√
1/ 3−−√
3−−√/1
3−−√ + 3−−√
3−−√ x 3−−√
1/ 3−−√
3−−√/1
Answers
GPT-4o mini
To determine which of the provided expressions are rational, let's evaluate each one:
1. \( \sqrt{3} + \sqrt{3} \)
This simplifies to \( 2\sqrt{3} \). Since \( \sqrt{3} \) is irrational, \( 2\sqrt{3} \) is also irrational.
2. \( \sqrt{3} \times \sqrt{3} \)
This simplifies to \( 3 \). This is a rational number.
3. \( \frac{1}{\sqrt{3}} \)
This is an expression where the denominator is an irrational number, thus \( \frac{1}{\sqrt{3}} \) is irrational.
4. \( \frac{\sqrt{3}}{1} \)
This simplifies to \( \sqrt{3} \), which is irrational.
From the analysis above, the only rational expression among the options is:
**\( \sqrt{3} \times \sqrt{3} = 3 \)**.
1. \( \sqrt{3} + \sqrt{3} \)
This simplifies to \( 2\sqrt{3} \). Since \( \sqrt{3} \) is irrational, \( 2\sqrt{3} \) is also irrational.
2. \( \sqrt{3} \times \sqrt{3} \)
This simplifies to \( 3 \). This is a rational number.
3. \( \frac{1}{\sqrt{3}} \)
This is an expression where the denominator is an irrational number, thus \( \frac{1}{\sqrt{3}} \) is irrational.
4. \( \frac{\sqrt{3}}{1} \)
This simplifies to \( \sqrt{3} \), which is irrational.
From the analysis above, the only rational expression among the options is:
**\( \sqrt{3} \times \sqrt{3} = 3 \)**.