Question

Prove that 5root 3 is irrational

Answer 1

Step-by-step explanation:

In order to prove 5√3 as an irrational number.

Let us assume 5√3 as a rational number.

let, 5√3 = a/b

( where a and b are coming primes and b is not equal to zero )

5√3 = a/b

√3 = a /b - 5

√3 = a-5/b

√3 = a-5b/b

here (R. H. S) is

in p/q form therefore it is a integer and (L. H. S) √3 is an irrational number.

Therefore it is a contradiction because of our false assumption.

so, we can conclude that 5√3 is an irrational number.

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