Prove that 8- root 2 is irrational
Answers
Answer:
Step-by-step explanation:
√2 is an irrational number
Suppose it can be written in the form of p/q, and q is not equal to zero.
When p and q are relative prime numbers
√2= p/q~~eq(1)
Where p and q are relative prime number
Taking square on both sides of eq(1)
2=p2/q2
Splitting q2 in two terms
2=p2/q.q
Now, taking one q on other side
2q=p2/q~~eq(2)
Since p and q being relative prime number, q cannot divide p and p2.
As l.h.s of eq(2) is an integer i.e; na
Hence, l.h.s of eq(2) is not equal to r.h.s.
Hence, out assumption is wrong.
So, it is proved that √2 is an irrational number.
Answer:
Step-by-step explanation:
root2 is an irrational number
Suppose it can be written in the form of p/q, and q is not equal to zero.
When p and q are relative prime numbers
√2= p/q~~eq(1)
Where p and q are relative prime number
Taking square on both sides of eq(1)
2=p2/q2
Splitting q2 in two terms
2=p2/q.q
Now, taking one q on other side
2q=p2/q~~eq(2)
Since p and q being relative prime number, q cannot divide p and p2.
As l.h.s of eq(2) is an integer i.e; na
Hence, l.h.s of eq(2) is not equal to r.h.s.
Hence, out assumption is wrong.
So, it is proved that √2 is an irrational number.