Q1 of 57 Page 29

Prove that is an irrational number.

Let us consider that 5 - √3 is a rational number.

Let 5 - √3 = a/b for b ≠ 0 ……………… (i)


Where a and b are co-prime integer numbers.


From (i) we can write as follows:


5 – a/b = √3



Now from the LHS we know that a and b are integral numbers and therefore the fraction will also be rational number which implies that √3 has to be a rational number. But we know that √3 is an irrational number.


So our assumption at the beginning of the problem is proved false.


So 5 - √3 is an irrational number.


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