Find continued product of `(sqrta+sqrtb)(sqrta-sqrtb)(a+b)(a^2+b^2)`

(sqrta+b)(sqrta-b) =

(sqrta + sqrtb)^2 = ?

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

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

(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)

If sqrta : sqrtb = sqrt3 : sqrt2 " and " sqrtb : sqrtc = sqrt3 : sqrt2 , then find the value of (sqrta + sqrtb ) : ( sqrtb + sqrtc) .

lim_(xto a) (sqrt(a + 2x) - sqrt(3a))/(sqrtx - sqrta)

If 3sqrta+3sqrtb+3sqrtc=0" then "(a+b+c)^(3)=