Question

how
$\sqrt{2}$
isn't rational number explain?​

Answer 1

to prove : √2 is irrational

let us assume that √2 is rational no.

√2=p/q where p ,q are integers and q is not equal to 0

√2=a/b where a,b are co primes and b is not equal to zero

cross multiplication

√2b=a

squaring both sides

2b^2=a^2 .eq1.

b^2=a^2/2. eq2

therefore, 2 divides a^2

2 must divide a by theorem 1.3

a=2m , where m is any integer

substitute the value of a in eq1

2b^2=4m^2

2b^2/4=m^2

b^2/2=m^2

therefore 2 divides b^2

then 2 must divide b

so, 2 is common factor of a&b

but a,b are co primes

so, our assumption was wrong and through this contradiction we prove that √2 is irrational

or its decimals are non terminating and non recurring