Q5 of 104 Page 1

Prove that following numbers are irrational :

√7 – √5

Let us assume - is rational

Let, - =


Squaring both sides, we get


2 =


12 - 2 =


2 = – 12


2 =


=



Since, rational ≠ irrational


This is a contradiction.


, Our assumption is incorrect.


Hence, is irrational.


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Without actually performing the long division, state whether the following rational numbers have terminating or non-terminating repeating (recurring) decimal expansion.