Question

prove that 3/2 root 5 is irrational​

Answer 1

Step-by-step explanation:

Let us assume that 3 + 2√5 is a rational number. This shows (a-3b)/2b is a rational number. But we know that √5 is an irrational number. So, it contradicts our assumption.

Answer 2

Answer:

Prove 3+2

5

is irrational.

→ let take that 3+2

5

is rational number

→ so, we can write this answer as

⇒3+2

5

=

b

a

Here a & b use two coprime number and b



=0.

⇒2

5

=

b

a

−3

⇒2

5

=

b

a−3b

∴

5

=

2b

a−3b

Here a and b are integer so

2b

a−3b

is a rational number so

5

should be rational number but

5

is a irrational number so it is contradict

- Hence 3+2

5

is irrational.