Friday, 20 December 2024

Class 10 -Prove √3 is a Irrational number.

 



Prove √3 is a Irrational number.

Proof:

Let √3 be a rational number.


So,  3=p ____ (1) q       

On squaring both sides

3=p2q2
q2= p23

3 is a factor of p2

3 is a factor of p.

Now, again let p = 3 c.

So,  3= 3 cq

On squaring both sides



3
= 9 c2q2




q
2
=3 c2






c
2
= q23




3 is factor of 
q2



3
 is a factor of q.

Here 3 is a common factor of p, q  both

 So p, q are not co-prime.

Therefore our assumption is wrong. 

3  is an irrational number.

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