Q27 of 180 Page 2

Prove that 5 is irrational.

Let us assume that 5 √2 is a rational number and can be written in the form of , where a and b are co – prime.


Therefore,



Here, on the right side is a rational number.


This implies that √2 is also a rational number but this contradicts the fact that √2 is an irrational number.


This contradiction has arisen because of the wrong assumption that we have made in the beginning.


Hence, 5√2 is an irrational number.


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