Question

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

Answer 1

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Answer 2

Answer:

√p + √q is  irrational

Step-by-step explanation:

let assume that

√p + √q is rational number

then

√p + √q  =  x/y

Squaring both sides

=> p + q  + 2√pq = (x/y)²

=>  2√pq = (x/y)² - p - q

=> √pq = (1/2)((x/y)² - p - q)

p, q are primes

=> √pq is irrational

now LHS = irrational

while RHS = rational

=> our assumption is not correct

=> √p + √q is not rational number

=> √p + √q is  irrational