Question

Who proved that √2 is irrational number.​

Answer 1

Answer:

To prove that √2 is irrational....

Step-by-step explanation:

Let us assume that √2 is rational, i.e, it can be expressed in the form of p/q where p and q are co-prime integers and q≠0.

So, √2=p/q

or,   p=q√2

Squaring both sides,

p²=2q²

Since p² is an even number and p is an integer, p is also an even number with factor of 2.

Let us write p=2m, where m is that factor which when multiplied with 2 results in p.

Then, (2m)²=2q²

Or,      4m²=2q²

Or,      q²=2m²

Since q² is an evennumber and q is a non-zero integer, q is also a multiple of 2.

Hence, p and q have common multiple 2 which contradicts our statement that √2 can be expressed in the form of p/q where p and q are co-prime integers with no other common factor than 1 and q≠0.

This contradiction has resulted because our presumption that √2 is a rational number is wrong.

Hence, √2 is irrational.

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