Prove that ✓p+✓q is irrational,where p,Q are primes.
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Let √p+√q is rational number
A rational number can be written in the form of a/b
√p+√q=a/b
√p=a/b-√q
√p=(a-b√q)/b
p, q are integers then (a-b√q) /b is a rational number.
So, √p is also a rational number.
But this contradicts the fact that √p is an irrational number.
so, our supposition is false
√p+√q is an irrational number
A rational number can be written in the form of a/b
√p+√q=a/b
√p=a/b-√q
√p=(a-b√q)/b
p, q are integers then (a-b√q) /b is a rational number.
So, √p is also a rational number.
But this contradicts the fact that √p is an irrational number.
so, our supposition is false
√p+√q is an irrational number
Answered by
4
Let √p+√q is rational number
A rational number can be written in the form of a/b
√p+√q=a/b
√p=a/b-√q
√p=(a-b√q)/b
p, q are integers then (a-b√q) /b is a rational number.
So, √p is also a rational number.
But this contradicts the fact that √p is an irrational number.
so, our supposition is false
√p+√q is an irrational number
A rational number can be written in the form of a/b
√p+√q=a/b
√p=a/b-√q
√p=(a-b√q)/b
p, q are integers then (a-b√q) /b is a rational number.
So, √p is also a rational number.
But this contradicts the fact that √p is an irrational number.
so, our supposition is false
√p+√q is an irrational number
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