Question

Prove that root 5 is irrational.​

Answer 1

Answer:

so it can be expressed in the form p/q where p,q are co-prime integers and q= 0

=> √5=p2/q2

=> 5q2 =q2

so 5 divides p

p is a multiple of 5

=>p=5m

=>p2 = 25m2--------

from equation (i) and (ii),we get,

5q2=25m2

=>q2=5m2

=>q2is a multiple of 5

=>q is a multipl of 5

hence,p,q have a common factor 5. This contradicts our assumption that they are co-primes. Therefore,p/qis not a rational number

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Answer 2

Answer:

Let us prove that √5 is an irrational number, by using the contradiction method. So, say that √5 is a rational number can be expressed in the form of pq, where q ≠0. So, let √5 equals pq. Where p, q are co-prime integers i.e. they do not have any common factor except '1'.