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Question

Show that 53 is an irrational number.

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Solution

Assume that 53 is a rational number. Then it can be expressed as a fraction,

53=pq

5pq=3

Where p and q are co-prime numbers and q0.

5qpq=3

It can be observed that 5qpq is a rational number because adding or subtracting two rational numbers gives a rational number but 3 is an irrational number which cannot be possible.

Therefore, the assumption is wrong.

Hence, 53 is an irrational number.


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