Question

prove root 57 is irrational​

Answer 1

Answer:

we prove this by using method of contradiction.

Step-by-step explanation:

latest latest resume to the contrary that root 57 is rational.

hence we can find coprime integers p and q such that,

root 57 = p/q

root 57q = p

squaring both sides we get ,

57 q^2 = p^2

therefore 57 divides p^2,

so 57 divides p.

so, p= 57c , where c is an integer.

substituting for p we get,

root 57q^2 = 57c^2

q^2 = 57c^2

this means 57 divides q^2

so 57 divides q.

therefore p and q have at least 57 as a common factor.

but this contradicts the fact that p and q are co primes.

discount addiction has arisen because of our incorrect assumption that root 57 is rational.

so ,we conclude root 57 is irrational.