Question

prove that √2 is an Ir-rational number​

Answer 1

Answer:

because it cannot give as the ratio of two integers

Step-by-step explanation:

√2= a/b

hcf = 1

(√2)^2=(a/b)^2

2=a^2/b^2

2b^2= a^2

2/a^2

2/a--------------eq 1

a=2c----------for some integers

a^2=4c^2

2c^2=4c^2

b^2=4c^2

2/b^2

2/b ------------eq 2

we obtain that 2 is factor of both and b so

from eq 1 and eq 2

√2= irrational number