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Question

Prove that 27 is irrational.


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Solution

Let us assume that 27 is a rational number.

27= 27×77=277( Rationalising)

Now,277=pq ( as rational no. can be written in the form of pq)

27=7pq
7=7p2q

Here LHS is irrational but RHS is rational.

This contradicts the statement.
Our assumption is wrong.

27 is an irrational number.



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