Question

prove that √5 irrational
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Answer 1

Step-by-step explanation:

Let us assume to contrary that √5 is rational .

So , √5 = p/q .

where , p and q are integers and co - prime numbers having no common factor other than 1 .

(√5)² = (p)²/(q)²

5 = p²/q²

5q² = p²

Clearly 5 divide p²

So , 5 divide p

Let p = 5m

5q² = (5m)²

5q²= 25 m

q² = 25 m / 5

q² = 5m

or

5m = q²

clearly 5 divide q²

so , 5 divide q

Thus , p and q have atleast 5 as a common factor . So , our assumption that√5 is rational is wrong .

So ,

√5 is irrational .

Hence proof