If a and b are positive natural numbers `(sqrta+sqrtb)(sqrta-sqrtb) = a-b`

(sqrta+b)(sqrta-b) =

(sqrta + sqrtb)^2 = ?

(a + b)(sqrta + sqrtb ) (sqrta - sqrtb)= "________"

In a triangle ABC, sqrta+sqrtb-sqrtc is

Simplify the following using multiplication and division properties of surds : (7sqrta-5sqrtb)(7sqrta+5sqrtb)

If (a+b) alpha sqrt(ab) , then show that (sqrta+sqrtb) alpha (sqrta-sqrtb) .

If a, b, c are in A.P., prove that : 1/(sqrtb+sqrtc), 1/(sqrtc+sqrta), 1/(sqrta+sqrtb) are also in A.P.

(a) If x gt a, y gt b and x + y = a + b , then find which one of (sqrtx + sqrty) and (sqrta + sqrtb) is greater ? (b) Which one of the two (sqrt21 + sqrt11) and (2sqrt5 + 2 sqrt3) is greater ? (c) Which one is greater root(3)(4) and root(4)(5) ? (d) Find the greatest and least numbers : 2 sqrt2, 3 root(3)(2), 2 root(4)(3), 2 root(6)(7)

Three positive numbers a,b,c are in A.P prove that 1/(sqrtb+sqrtc) , 1/(sqrtc+sqrta) and 1/(sqrta+sqrtb) are aslo in A.P