Question

proof of √3 is irrational( class 10) (wanted step by step answer )​

Answer 1

Step-by-step explanation:

so let √3 be a rational no.

then, √3 must be equal to p/q where p and q are integers and have no. common factor other than 1.

then

√3=p/q

√3 ×q =p

squaring both sides

3q²=p² ....eq.(I)

hence 3is a factor of p²

then 3 must be a factor of p

so let p=3c

put this value in eq.l

3q²=(3c)²

q²=3c²

here we got that 3 is also a factor of q²

then it must be a factor of q

hence contradiction arises as 3 is factor of both p and q

so, √3 is not a rational no. it's an irrational no.

*proved*

hope this helped you