Prove that sqaure root of 3 is an irrational number... and
Answers
Answer:
Let us assume to the contrary that v3 is a rational number.
It can be expressed in the form of p/q
where p and q are co-primes and q 0.
V3 = p/q
3 = p?/q? (Squaring on both the sides)
3q? = p?.
..(1)
This means that 3 divides p2. This means that 3 divides p because each factor should appear two times for the square to
exist.
So we have p = 3r
where r is some integer.
p? = 9r2.
from equation (1) and (2) 3q? = 9r2
q3 r2
0.6KB/s *
Where q 2 is multiply of 3 and also q is multiple of 3.
Then p, q have a common factor of 3. This runs contrary to their being co prime.
Consequently, p/q is not a rational number. This demonstrates that v3 is an irrational number.
Answer:
Let us assume to the contrary that v3 is a rational number.
It can be expressed in the form of p/q
where p and q are co-primes and q 0.
V3 = p/q
3 = p?/q? (Squaring on both the sides)
3q? = p?.
..(1)
This means that 3 divides p2. This means that 3 divides p because each factor should appear two times for the square to
exist.
So we have p = 3r
where r is some integer.
p? = 9r2.
from equation (1) and (2) 3q? = 9r2
q3 r2
0.6KB/s *
Where q 2 is multiply of 3 and also q is multiple of 3.
Then p, q have a common factor of 3. This runs contrary to their being co prime.
Consequently, p/q is not a rational number. This demonstrates that v3 is an irrational number.