Question

Prove that root 2 is irrational​

Answer 1

To prove: √2 is irrational

Solution: Let √2 be a rational number.

so, it can be expressed in the form a/b where b not equals to 0 and a and b should not have any common factor.

so,√2= a/b

squaring both sides we get,

2=a^2/b^2

or, 2b^2 = a^2....(i)

Thus 2 is a factor of a

Now, let a=2c

putting a=c in (i) we get:

2b^2= 4c^2

or, b^2= 2c^2

so, 2 is a factor of b as well as a

This violates the rule for being a rational number

Thus our supposition was wrong.

Hence √2 is an irrational number. proved

This is the answer....

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Answer 2

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We can prove it irrational by contradiction.