prove that root 2 is irrational ?
Answers
Answered by
2
find a irrational number divided by 1 any number so come ur ans in decimal
Answered by
4
Asusume that √2 is a rational no.
Then,√2=p/q, where p&q are co prime
Now, squaring both sides
√2²=p²/q²
2= p/q
p²=2q²-(i)
2divides p²
2divides p-(ii)
Let p= 2m
p²=4m²
Putting values of p² in -(i)
We have,
4m²=2q²
2divides q²
2divides q -(iii)
Thus 2divides both p&q [from ii & iii]
it means 2 is a common factor of p & q
This contradicts the assumption that p & q are coprimes
Thus √2 is not a rational no.
Then,√2=p/q, where p&q are co prime
Now, squaring both sides
√2²=p²/q²
2= p/q
p²=2q²-(i)
2divides p²
2divides p-(ii)
Let p= 2m
p²=4m²
Putting values of p² in -(i)
We have,
4m²=2q²
2divides q²
2divides q -(iii)
Thus 2divides both p&q [from ii & iii]
it means 2 is a common factor of p & q
This contradicts the assumption that p & q are coprimes
Thus √2 is not a rational no.
Similar questions