Q13/051) Prove that for integers n,m and p if √ (n) + √(m) = p then √(n) and √ (m) are integers

√ (n) + √(m) = p

ð     √ (n) = p -  √(m)

ð     n = p^2 – 2p √(m) + m^2

ð     √(m) = (p^2 +m^2 –n)/ (2p)

ð     √(m) is rational

Now √(m) is rational so there exists integers such that m = s/t

So m = s^2/t^2 or s^2 = mt^2

As left hand side is a square and so RHS is s square and hence m has to be s square then √(m) is rational and √ (n) = p - √(m) is also rational.