Question

show that √3 is an irrational number​

Answer 1

Answer:

hyyy

Step-by-step explanation:

ANSWER

Let us assume on the contrary that

√3is a rational number.

Then, there exist positive integers a and b such that √3 = a/b

where, a and b, are co-prime i.e. their HCF is 1

Now, √3 =ba

⇒3 = a² / b²

⇒3b²=a²

⇒3 divides a² [∵3 divides 3b²]

⇒3 divides a...(i)

⇒a=3c for some integer c

⇒a²=9c²

⇒3b² =9c² [∵a² =3b² ]

⇒b²=3c²

⇒3 divides b²[∵3 divides 3c² ]

⇒3 divides b...(ii)

From (i) and (ii), we observe that a and b have at least 3 as a common factor. But, this contradicts the fact that a and b are co-prime. This means that our assumption is not correct.

Hence, 3 is an irrational number.

Answer 2

Answer:

nice answer....................