`[(a/b)^(sqrt(p)+sqrt(q))]^(sqrtp-sqrtq)[(a/b)^(sqrt(q)+sqrt(r))]^(sqrtq-sqrtr)[(a/b)^(sqrt(r)+sqrt(p))]^(sqrtr-sqrtp)`

(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))

cot(7((1)/(2))^(@)=sqrt(p)+sqrt(q)+sqrt(r)+sqrt(s)

If p and q are distinct primes and xxDelta = |(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)|xx

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

The conjugate surd of sqrt(a)+b is sqrt(a)-b b- "sqrt(a) sqrt(a)+sqrt(b) sqrt(a)-sqrt(b)

Compare the surds (i) A=sqrt(10)-sqrt(5),B=sqrt(19)-sqrt(14) (ii) P=sqrt(10)+sqrt(5),Q=sqrt(8)+sqrt(7)

Compare the surds (i) A=sqrt(10)-sqrt(5),B=sqrt(19)-sqrt(14) (ii) P=sqrt(10)+sqrt(5),Q=sqrt(8)+sqrt(7)

If a,b,c are in A.P then (1)/(sqrt(b)-sqrt(c)),(1)/(sqrt(c)-sqrt(a)),(1)/(sqrt(a)-sqrt(b)) are in

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 =