Question

prove root 3 is am irrational number​

Answer 1

let assume root 3 is rational number..

Root 3 = a/b where a and b are integers and coprimes.

Root 3 * b = a

Square LHS and RHS

3b2 = a2

b2 = a2/3

Therefore 3 divides a2 and 3 divides a.

Now take ,

a = 3c

Square ,

a2 = 9c2

3b2 = 9c2

b2/3 = c2

Therefore 3 divides b2 and b

Hope it's helpful ☺️✔️

Answer 2

Step-by-step explanation:

let us assume root 3 is rational

root3 =a/b (where b is not. equal to zero)

root3 b= a

squaring both side

3b²=à². (wher 3 is co prime)

3divides a²

3 divides a

put a =3m

,put in 3b²=a²

3b²=3m²

b²=3m

here 3 divides b²

3 divides b

here we conclude 3 divides both a and b we conclude that 3 is co prime no

aur consumption is wrong

root 3 is irrrational number