Question

prove that √3 is an irrational number​

Answer 1

Answer:

Let √3be a rational no.which is in the form

P/q,p=0

proof:

√3 = P/q

squaring both side

= (√3)² = (p/q)²

= (√3q)² = (p)²

= 3q² = p² ------(i)

= so if 3 is the factor of p²

then 3 is also a factor of p ----(ii)

=> Let p = 3m (where m is any integer)

squaring both side,

(p)² = (3m)²

p² = 9m²

putting the value of p² in equation ( i )

= 3q² = p²

= 3q² = 9m²

= q² = 3m²

q² = 3m²So,

q² = 3m²So,if 3 is factor of q²

q² = 3m²So,if 3 is factor of q²then, 3 is also factor of q

q² = 3m²So,if 3 is factor of q²then, 3 is also factor of qSince3 is factor of p & q bothSo, our assumption that p & q are co- prime is wrong

q² = 3m²So,if 3 is factor of q²then, 3 is also factor of qSince3 is factor of p & q bothSo, our assumption that p & q are co- prime is wronghence,. √3 is an irrational no.