Question

S.T √2 is a irrational
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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Let, √2 be rational

√2=a/b where a and b are integers , HCF(a,b)=1 and b≠0

Now,√2=a/b

=>(√2)²=(a/b)²[on squaring both sides]

=>2b²=a² .........(I)

=>2 divides a² [2 divides 2b²]

=>2 divides a

putting a=2c for some integers from (I)

a²=(2c)²

2b²=4c²

b²=2c²

=> 2 divides b²...... (ii)

2 divides b

so from (I) and (ii) we get

2 is a common factor of a and b.

But, this contradicts the fact that a and b have no common factor other than 1.

it is a contradiction.

so, our assumption is wrong.

√2 is not rational.

Hence,√2 is irrational. [proved]