Question

Which of the following is rational?
A. The square root of 3 over 1
B. The square root of 3 times the square root of 3
C. The square root of 3 plus the square root of 3
D. 1 over the square root of 3

Answer 1

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

A. \(\frac{\sqrt{3}}{1}\) - Since \(\sqrt{3}\) is an irrational number, this expression is also irrational.

B. \(\sqrt{3} \times \sqrt{3}\) - This simplifies to \(3\), which is a rational number.

C. \(\sqrt{3} + \sqrt{3}\) - This is equal to \(2\sqrt{3}\), which is irrational since \(\sqrt{3}\) is irrational.

D. \(\frac{1}{\sqrt{3}}\) - This is also irrational because it can be rationalized to \(\frac{\sqrt{3}}{3}\), which still involves \(\sqrt{3}\).

Thus, the only rational expression among the options is:

**B. The square root of 3 times the square root of 3** (which equals \(3\)).