Question

Prove that √p+√q is irrational,where p,q are primes

Answer 1

Answer:

Step-by-step explanation:

=> √q = a – √p Squaring on both sides, we get q = a2 + p - 2a√p => √p = (a2 + p - q)/2a, which is a contradiction as the right hand side is rational number, while √p is irrational. Hence, √p + √q is irrational.

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Answer 2

let √p is rational no.

I. e a/b =√p , b not equal to the zero, a and b

should be coprime

a =√pb

sq. on both sides

a^2 = pb^2

I. e. p is the factor of a

so let a be the p

p^2= pb^2

p=b^2

i.e p is the factor of b

but a and b should be coprime

so our supposition is wrong

i.e √p is an irrational no.

as we know that

i.r+ r = i.r

so √p + √ q is an irrational no

hence proved

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