CBSE Class 10 Answered
prove √5 is irrational number
Asked by appusingh0840 | 29 Oct, 2023, 01:14: PM
Expert Answer
Let √5 is a rational number.
Then we can write , √5 = p/q
where p and q are integers, q ≠ 0 and p and q are co-prime
( i..e. p and q do not have any common factor othr than 1 )
By squaring both sides we get , .......................(1)
From above expression , we get 5 is factor of p .
hence we write , p = 5 c and p2 = 25 c2
Hence eqn.(1) becomes
Hence q is divisible by 5 , or 5 is a factor of q .
Hence we get 5 is afctor of p and aloso factor of q .
But we have started with the assumption p and q are co-prime .
Hence √5 ≠ p/q if p and q are integers
Hence √5 is not a rational number and it is irrational number .
Answered by Thiyagarajan K | 29 Oct, 2023, 04:18: PM
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