Q14 of 44 Page 1

Prove that 2 - 3√5 is an irrational number. (CBSE 2010)

Let x = 2 - 3√5 and let us assume that x is rational.


For x to be rational, .


So,





Now, x is rational, will also be rational. But √5 is irrational. So, the statement made is wrong. Hence, 2 - 3√5 is irrational.


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