Question

Prove that
$\sqrt{5}$
is irrational

Answer 1

heya !!

here's your solution :-

______________________

Let √5 be a rational number.

Suppose " a " and " b " are co - prime integers.

So , √5 = a / b

=》a = b √5

On squaring both sides , we get

=》a^2 = 5 b^2

■ hence 5 is the of a^2

=》Also 5 is a factor of " a "

Let ,

=》a = 5 c ( "c" is some integer )

On squaring both sides , we get

=》a^2 = 5c^2

Since we have proved that a^2 = 5 b^2.
Put the value on above eq.

=》5 b^2 = 25 c^2

=》b^2 = 5 c^2

■ 5 is a factor of b^2

=》also 5 is a factor of b

■ Hence 5 is a common factor of a , b.

But this contradicts the fact that a and b are co - primes.

☆ So √5 is irrational.

_______________________

hope it helps u !!!!

thanks for asking :)

☆ be brainly ☆