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CBSE Class 10 Answered

show that root 3 is an irrational number
Asked by ajayrath7 | 12 Mar, 2019, 11:52: AM
answered-by-expert Expert Answer
Let us start with the contrary, √3 is a rational number.
 
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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