Question

prove 3/2√5 is irrational​

Answer 1

Step-by-step explanation:

Let √5 be a rational number .

√5=a/b        (where a and b are co primes)

Squaring both sides,

5=a^2/b^2

5 b^2=a^2  -----------------( 1 )

Thus 5 divides a.

a=5 c for some integer c.

Substitute value of a in ( 1 ),

b^2=5 c^2

Thus 5 divides b.

This proves that a and b are not co primes and thus √5 is an irrational number.

Let 3/2√5 be a rational number.

3/2√5=a/b

1/√5=2a/3b

√5=3b/2a

Here √5 is expressed as a rational number but it contradicts the fact that √5 is an irrational number.

Therefore 3/2√5 is an irrational number.