Question

prove that√3 is a irrational number​

Answer 1

Answer:

Let, √3 be a rational number.

So, √3=p/q,

where; p≠0 and p and q are

co-prime numbers.

or p=√3q

On squaring both sides:

p²=3q²

» 3 divides p² and p

So, we can write that:

p=3x....(1)

Now, as p²=3q²

» p²=3q²=(3x)²

» 3q²=9x²

or q²=3x²

» 3 divides q² and q

But, p and q must be co prime number so as for √3 to be a rational.

This contradiction is due to our wrong assumption, that √3 is rational.

Hence, √3 is proved to be irrational.

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