Idk what this is but please help

[haughty lotus]

A rational number is any number that can be written in the form a/b where a and b are both integers and b>0

[haughty lotus]

[blissful ocean]

thnks

[south badger]

@blissful ocean. Knowing the definitions and having examples will help

[blissful ocean]

thanks alot

[coarse shuttle]

Since it is really not that easy to proof i will tell you: Pi is irrational.

[surreal tangle]

-root9, root5/2, root(16/100) are NOT rational

[coarse shuttle]

Congrats, you named 2 of the 3 rational numbers...

[fierce hull]

b doesn’t have to be greater than 0 it can be any integer but 0. So it should be b≠0

[coarse shuttle]

If a is any integer and b is an integer greater than 0 you can express any rational number

[fierce hull]

“Greater than 0” means that b cannot be negative according to what you said and it has to be an integer

[coarse shuttle]

Yes but a can

[fierce hull]

Ik

[coarse shuttle]

So a/b can always be negative or positive

[fierce hull]

But it depends on the number

If for example you have -6, then it can be expressed as -12/2 or 12/-2

But not -12/-2

[coarse shuttle]

Its useful to define it with that "restriction" as you are still able to express every rational number but you have properties such that for every a/b and p/q with a and b having no common factor, and p and q having no common factor: a=p and b=q.

[fierce hull]

But they have a case where b<0

[coarse shuttle]

yeah i didnt express myself correctly. if you have b<0 that doesnt mean it cant be a rational number, but you can always turn it into a form where b>0

[fierce hull]

Ohhh

Ok that makes sense

[coarse shuttle]

canonical form can also be used to proof that sqrt(n) is irrational for every natural number n that isnt equal to a^2 where a is a natural number.

[coarse shuttle]

anyway, back to the original question, here is how i would solve it (i guess you have already done/thought about it):
||7/4 is rational since both 7 and 4 are integers
square root of 10 is irrational since every square root of a natural number wich isnt a perfect square is irrational
negative square root of 9 is rational since it can be expressed as -3/1 wich is rational
(square root of 5)/2 is irrational since square root of 5 is irrational and dividing an irrational number by 2 doesnt make it rational
square root of (16/100) is rational since it can be expressed as 4/10 wich is rational
pi is irrational, although proving it requires calculus and isnt as easy as the other ones||

first one is the proof of the claim for square root of 10 and the second screenshot is proof that pi is irrational, just for sake of completeness.

(those proofs arent made by me)

[fierce hull]

Nice!

[still yoke]

• root 9 is rational and root 16/100 is rational

[surreal tangle]

sorry