1.

Prove that√2 is irraational​

Answer»

<P>Answer:

proof = let us assume that √2 is rational no.

Step-by-step explanation:

since rational no √2= p/q ; hcf(p,q) = 1 ; q not EQAL to 0 and p, q belongs to integers

i. e. p/q = √2

s. o. b. s

p2/q2= 2

p2=2q2

here 2 divides p2

2 divides p......... 1

since 2 divides p

let p be 2m where m is some integer

from above 2m = q2

s. o. b. s

q2= 4m2

q2= 2m2

here 2 divides q2

2 divides q

since here 2 divides both q and p

hcf(p,q)=2

but above hcf of p, q is 1

this contradiction arises if our assumption is wrong

therefore our assumption is wrong

and hence √2 is irrational



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