Question

Which is rational? Responses 10 square root of 10 2π (2 times pi) 2 pi (2 times pi) 3 square root of 3

Answer 1

To determine which of the given numbers is rational, we need to look at each one:

1. \(10 \sqrt{10}\) - This is not rational because \(\sqrt{10}\) is an irrational number, and multiplying an irrational number by a rational number (10) results in an irrational number.

2. \(2\pi\) - \(\pi\) is an irrational number, so \(2\pi\) is also irrational.

3. \(2 \pi\) - This is the same as the previous entry, \(2\pi\), and is also irrational.

4. \(3 \sqrt{3}\) - \(\sqrt{3}\) is an irrational number, and multiplying it by 3 (a rational number) results in an irrational number.

Since all the options provided involve either irrational numbers or a product that includes an irrational number, none of the given numbers are rational.

Thus, none of the responses are rational numbers.