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show that root 3 is an irrational number
Asked by ajayrath7 | 12 Mar, 2019, 11:52: AM Expert Answer

Hence √3 = a/b  ..................(1)

where a and b are prime integers and no comman factor between a and b.

hence √3b = a

By squaring both sides,  3b2 = a2  or  a2 / 3 = b2 ..............(2)

eqn.(2) shows 3 is a factor of a2 .  If a is a prime number, then 3 also should be factor of a.

If 3 is a factor of a, then this contradicts the assumption we made for eqn.(1), that a is a prime number.

Hence √3 is not a rational number , it is an irrational number
Answered by Thiyagarajan K | 12 Mar, 2019, 02:52: PM
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