Question

prove that
$\sqrt{5}$
is a irrational.
​

Answer 1

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Answer 2

Answer:

let us assume the √5 is a rational number

Now, let √5=a/b,where a and b are coprime and

b≠0

squaring both sides

(5)²=(a/b)²

b²3=a²

b²=a²5

a² is divisible by 5

a is also divisible by 5

Let,a=3m for some integer m

√5=5m/b

squaring both sides

(√5)²=(5m/b)²

b²=25m²/5

b²/5=m²

b is divisible by 5

a is divisible by 5

we can conclude that 5 is a common factor of both a and b

but this contradicts our supposition a and b are coprime

hence,√5 is irrational

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