Prove that root 5 -2root 3 is anirrational
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Hello,
PROOF :-
Let root 5 - 2 root 3 be a rational number
So
It can be expressed in the form of p/q where q≠0 and p, q are Co primes as well as integers.
So,
For some integer
The RHS is a rational number
While root15 (LHS) is not a rational number.
Hence,
It is a contradiction
Our assumption was wrong.
So
Root 5 - 2 root 3 is not a rational number. It is an irrational number.
Hence, proved
Hope this will be helping you ✌️
PROOF :-
Let root 5 - 2 root 3 be a rational number
So
It can be expressed in the form of p/q where q≠0 and p, q are Co primes as well as integers.
So,
For some integer
The RHS is a rational number
While root15 (LHS) is not a rational number.
Hence,
It is a contradiction
Our assumption was wrong.
So
Root 5 - 2 root 3 is not a rational number. It is an irrational number.
Hence, proved
Hope this will be helping you ✌️
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