Question

how can an irrational number represent an exact length

Answer 1

So basically you are asking how can the circumference of a circle with radius one with be 2pi?

Answer 2

all exact lengths are irrational
rationals are only an approximation

Answer 3

not really @freckles

Answer 4

but you do though pi is irrational right?

Answer 5

know*

Answer 6

could you perhaps add more detail @@satellite73

Answer 7

i do know @freckles

Answer 8

*@satellite73

Answer 9

@satellite73

Answer 10

I don't know if I understand. If you know a circle with radius 1 can have circumference 2pi and you know that pi is irrational, then why are you questioning if irrationals can represent exact lengths?

Answer 11

my math teacher would like us to use triangles @freckles

Answer 12

oh ok
well let's thing about a square for a sec

Answer 13

ok @freckles

Answer 14

say with a side length 1

and by Pythagorean thm we have
\[1^2+1^2=hyp^2 \\ 1+1=hyp^2 \\ 2=hyp^2 \\ \sqrt{2}=hyp\]

this triangle has a side length of sqrt(2)