Question

Which expression is rational?
4.121221222, square root of the quantity five squared minus four squared, two plus square root of the quantity seven squared minus twelve, 1.193744502

Answer 1

On the page you copied this question from, does the 4.121221222
have several dots after it like this:
4.121221222....
or no dots exactly like you wrote it? It's important. With no dots, that would be rational,..., with the dots that thing will not be rational.

Answer 2

no but the 1.193744502 does

Answer 3

The rule is this: Any decimal that goes on forever (...'s mean it goes on forever) and does not have some kind of repeating pattern ( like 2.727272727272....) is NOT rational.

Answer 4

So, 1.193744502... is not rational, 4.121221222 is rational

Answer 5

but if i copy and paste it this is what it says: The infinite non-repeating decimal four point one two one two two one two two two dot dot dot. When i just type it, it says: 4.121221222

Answer 6

so im really confused

Answer 7

oh, okay! so it does go on forever. That is not rational then. And there is no repeating pattern because the number of 2's keeps getting larger.
4.12122122212222122222.... is irational
4.122122122122122... would be rational because the pattern "122" keeps going forever.

Answer 8

so then which one would be rational?

Answer 9

Lets look at " square root of the quantity five squared minus four squared "
What to you get when you calculate that?

Answer 10

how am i suppose to calculate it?

Answer 11

\[\sqrt{5^{2}-4^{2}}=\sqrt{25-16}=\sqrt{9}=3\]

Answer 12

Is 3 rational?

Answer 13

Does 3 have a decimal part attached to it that goes on forever? No. 3 is just 3. It's rational.

Answer 14

thank you!

Answer 15

sure no problem