Question

Prove that √2 is a irrational number​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Let us assume by contradiction method that √2 is a rational number.

Therefore,

√2 = a/b ( where a and b are co prime numbers)

b√2 = a

By squaring both sides

2b^2 = a^2 ----------------(1)

Now, if 2 divides a^2 then 2 will divide a also.

2c= a

By sqauring both sides

4c^2 = a^2

Now putting the value of a^2 from (1)

4c^2 = 2b^2

2c^2= b^2

Now if 2 divides b^2 then 2 divides b also.

here, a and b have 2 as their factors

But this contradicts the fact that a and b does not have any common factor other than 1.

Since our assumption is wrong.

Therefore √2 is irrational.

Hence , proved.

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