Question

prove that
$\sqrt{5}$
is irrational
​

Answer 1

Step-by-step explanation:

Let us assume that √5 is a rational number.

we know that the rational numbers are in the form of p/q form where p,q are coprime numbers.

so,√5=p/q

p=  √(5)q

we know that 'p' is a rational number. so  √(5)q must be rational since it equals to p

but it doesnt occurs with  √(5)q since its not an integer

therefore, p is not equal to √(5)q

this contradicts the fact that √(5) is an irrational number

hence our assumption is wrong and √(5) is an irrational number