If p and q are distinct primes and `Delta = |(sqrt(pq),p i,q+sqrt(pq)),(psqrt(q),sqrt(p)+psqrt(p)i,qsqrt(p)+sqrt(p) qi),(qsqrt(p), sqrt(p)+psqrt(q)i,qsqrt(q)+p i)|`

sqrt(x^(p-q))sqrt(x^(q-r))sqrt(x^(r-p))=1

[((a)/(b))^(sqrt(p)+sqrt(q))]^(sqrt(p)-sqrt(q))[((a)/(b))^(sqrt(q)+sqrt(r))]^(sqrt(q)-sqrt(r))[((a)/(b))^(sqrt(r)+sqrt(p))]^(sqrt(r)-sqrt(p))

If x=(sqrt(p+q)+sqrt(p-q))/(sqrt(p+q)-sqrt(p-q)) find the value of qx^(2)-2px+q

(i) (a^(p+q))^(p-q) (a^(q+r))^(q-r)(a^(r+p))^(r-p) (ii) [(a/b)^(sqrt(p)+sqrt(q))]^(sqrt(p)-sqrt(q))[(a/b)^(sqrt(q)+sqrt(r))]^(sqrt(q)-sqrt(r)) [(a/b)^(sqrt(r)+sqrt(p))]^(sqrt(r)-sqrt(p))

If (sqrt(p+2q)+sqrt(p-2q))/(sqrt(p+2q)-sqrt(p-2q)) , then show that qx^2-px+q=0

If x=(sqrt(p+q)+sqrt(p-q))/(sqrt(p+q)-sqrt(p-q)) then find the value of qx^(2)-2px+q

If (sqrt(7)+2sqrt(3))/(2sqrt(7)-sqrt(5))=(c+sqrt(p)+sqrt(q)+sqrt(r))/23(p < q < r), where p, q r are rational numbers, then q+ r - p =

If p and q are the roots of the equation lx^2 + nx + n = 0 , show that sqrt(p/q) + sqrt(q/p)+ sqrt(n/l) = 0 .

If p ,\ q are prime positive integers, prove that sqrt(p)+sqrt(q) is an irrational number.

If (sqrt(7)+2sqrt(3))/(2sqrt(7)-sqrt(5))=(c+sqrt(p)+sqrt(q)+sqrt(r))/(23)(p lt q lt r) , where p,q,are rational numbers, then q+r-p =