Question

how can we show that
$\sqrt{5}$
is irrational

Answer 1

→ let us assume that √5 is a rational number .

therefore,

→√5=p/q

( where p and q are integers and q≠0 ,also they are co prime numbers)

→ on squaring,

→5q²= p²

→p² is divisible by 5

p is also divisible by 5

now let p=5a

So,


5q²= (5a)²

q²= 5a²


→q² is divisible by 5

q is also divisible by 5

→i.e p and q has atleast 5 as their common factor,

→but this contradicts the fact that p and q are co prime numbers.

Thus our assumption is wrong.

Hence √5 is an irrational number.

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