which of the following is ratinoal?

Question

3−−√ + 3−−√
3−−√ x 3−−√
1/ 3−−√
3−−√/1

Answer 1

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:

\( \sqrt{3} \times \sqrt{3} = 3 \).