Given that sqrt 3 is irrational prove that 5+4 sqrt 3 is an irrational
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Given :-
is an irrational number.
To prove :-
is an irrational number.
Proof :-
Let is a rational number.
Then, it can be expressed in the form of p/q where p and q are co primes and .
Since,
transforming 5 on R. H. S
Also,
we know that every operation of rational is an rational number.
Subtraction of rational is also rational.
But here, L. H. S is irrational since, √3 is an irrational number (given)
And R. H. S is rational number .
LHS ≠RHS
This contradiction is arisen due to our wrong assumption .
hence, is an irrational number proved...
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