Question

√12/5 is rational or irrational

Answer 1

Answer:

Root 12/5 is irrational

Step-by-step explanation:

Answer 2

Answer:

Irrational

Step-by-step explanation:

let root 12 rational

root 12 = a/b, where a and b are coprime and b is not equal to 0

√12=a/b

√12b= a

12b^2 = a^2

12 divides a^2

12 divide a

Again,

a = 12c

a^2= 144c^2

12b^2 = 144 c^2

b^2 = 12c^2

12 divides b^2

12 divide b

We know that a and b r coprime so they should not have any factor except 1 and itself. But they have factors of 12. This shows that √12 is rational. But this contradicts the fact that √12 is irrational. This contradiction arises because of our wrong assumption that √12 is rational.

Hence √12 is irrational.

Anything divided by an irrational is also irrational.

Hence √12/5 is also Irrational.

Hope this helped you!!