Question

Prove that √3/2 is an irrational number.

Answer 1

Step-by-step explanation:

Let us assume, to the contrary, that 3

2 is rational. Then, there exist co-prime positive integers a and b such that 3

2 = b

a⇒

2 = 3b

a⇒

2 is rational

...[∵3,a and b are integers∴

3b a is a rational number]

This contradicts the fact that

2 is irrational.

So, our assumption is not correct.

Hence, 3

2 is an irrational number.

Answer 2

Answer:

Let √3 / 2 be rational, so, it can be expressed as p/q where, p and q are co prime numbers.

√3 / 2 = p / q

or, √3 = 2p / q

Since, p , q , and 2 are rational so √3 is rational.

This contradict the fact that √3 is irrational.

So, √3 / 2 is irrational.