Question

Which of the following is rational would it be square root root three times square root three or one over square root three or square root root three over one or square root 3+ square root three

Answer 1

To determine which of the given options are rational, let's analyze each one:

1. **Square root of 3 times square root of 3**:
\[
\sqrt{3} \times \sqrt{3} = 3
\]
(which is a rational number).

2. **One over square root of 3**:
\[
\frac{1}{\sqrt{3}}
\]
(this is not a rational number because \(\sqrt{3}\) is irrational. The result is also irrational).

3. **Square root of 3 over 1**:
\[
\frac{\sqrt{3}}{1} = \sqrt{3}
\]
(which is irrational).

4. **Square root of 3 plus square root of 3**:
\[
\sqrt{3} + \sqrt{3} = 2\sqrt{3}
\]
(this is also irrational, since \(\sqrt{3}\) is irrational, and multiplying an irrational number by a rational number remains irrational).

Thus, among the given options, the only rational expression is the **square root of 3 times square root of 3**, which equals **3**.