# What is a Good Pasta Number™?

This puzzle is inspired by JLee's What is a Word/Phrase™ series and the subsequent "Number" variants. (Actually, I'd originally tried to create a more original puzzle using the same idea, but it turned into another one of these. Sigh. Maybe the types of numbers given lend this somewhat more novelty.)

If a positive real number obeys a special rule, I call it a Good Pasta Number™. Here are some examples:

A good, solid pasta! Yeah! You are a horrible cook
$$6\sqrt{6}$$ $$3\sqrt{5}$$
$$6$$ $$8$$
$$3\sqrt{6}$$ $$6\sqrt{3}$$
$$\frac{3\sqrt{2}+\sqrt{6}}{2}$$ $$\frac{3\sqrt{6}+\sqrt{2}}{2}$$
$$3\sqrt{50-22\sqrt{5}}$$ $$3\sqrt{50+22\sqrt{5}}$$
$$9\sqrt{3}-3\sqrt{15}$$ $$18\sqrt{3}-6\sqrt{15}$$
$$\frac{42\sqrt{6}}{23}$$ $$\frac{56\sqrt{6}}{19}$$
$$\frac{15\sqrt{6}-18\sqrt{3}+135\sqrt{2}-162}{14}$$ $$\frac{15\sqrt{30}-18\sqrt{15}+135\sqrt{10}+30\sqrt{6}-162\sqrt{5}-36\sqrt{3}+270\sqrt{2}-384}{14}$$

There are many more Good Pasta Numbers™ not shown above, but only a finite amount.

Which numbers make a good pasta™?

Note:

There's nothing hidden in the flavortext other than a very subtle connection (not really a clue); this really is just a normal "What is a _______" puzzle. I like making my puzzles fun to read. Also, the property is specific to the numbers themselves, and not any specific representation of the aforementioned numbers.

• In the fifth row, the two numbers are Galois conjugate. Therefore I suppose that all your numbers are considered as real numbers and the square roots are positive ones. It might be useful to clarify this. Aug 5, 2022 at 14:21
• Uh, I'm not exactly sure what needs clarification. I already said "if a positive real number obeys a special rule," and square roots of positive numbers are positive by definition in most contexts. Aug 5, 2022 at 15:23
• Sorry, you are right, I missed the "positive real number" part. Aug 5, 2022 at 16:41