Question

Prove root 2 irrational in easy method.

Answer 1

Step-by-step explanation:

assuming that √2 is a rational number

so,√2 = m/n

take m and n as integers and it is greater than 1

now, √2 = m/n

now square both side

if we square √2 square will be cancelled

and m/n will become m^2/n^2

now 2 = m^2

/n^2

now take n^2 to the left

m^2 = 2n^2

now bring the constant out

m = 2k

now multiple with 2 and square on both sides

(2k)^2 = 2n^2

4k^2 = 2n^2

n^2= 4k^2

/2

= n^2 = 2k^2

now both m and n are = 2

so √2 is a irrational number