Question

prove √3 an irrational number​

Answer 1

Answer:

take the solution from it.. .. R's Agarwal class10 PG 27

Answer 2

Answer:

If possible ' Let, root 3 is an rational number

Let P/q = root 3 (where p and q are

coprime, q not=0

P= root 3 q

Squaring on both sides

p2=3q2

3 is the factor of p2

3 will be the factor of p ____(1)

Let p= 3k

(3k)2= 3q2

9k2=3q2

Dividing by 3 on both sides

3k2=q2

q2= 3k2

3 is the factor of q2

3 will be the factor of q____(2)

From (1) and (2) ,we get,

3 is the common factor of p and q

So, it opposes our supposition that p and q are coprimes

Hence root 3 is an irrational number