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# 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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