`sqrt(7/8) sqrt((11)/(6))`

Simplify the following expressions. (i) (5+sqrt(7))(2+sqrt(5)) (ii) (5+sqrt(5))(5-sqrt(5)) (iii) (sqrt(3)+sqrt(7))^2 (iv) (sqrt(11)-sqrt(7))(sqrt(11)+sqrt(7))

Simplify: -sqrt((-7)/(4))-sqrt((-1)/(7))

Evaluate : (1)/(3-sqrt(8)) -(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2).

Let T = (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7)) +(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)+2) then-

Show that : (1)/(3-2sqrt(2))- (1)/(2sqrt(2)-sqrt(7)) + (1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5 .

{:("Quantity A","Quantity B"),((sqrt6xxsqrt(18))/(sqrt9),(sqrt8xxsqrt(12))/(sqrt6)):}

If the ellipse (x^2)/(a^2-7)+(y^2)/(13=5a)=1 is inscribed in a square of side length sqrt(2)a , then a is equal to 6/5 (-oo,-sqrt(7))uu(sqrt(7),(13)/5) (-oo,-sqrt(7))uu((13)/5,sqrt(7),) no such a exists

Show that: 1/(3-sqrt(8))-1/(sqrt(8)-sqrt(7))+1/(sqrt(7)-sqrt(6))-1/(sqrt(6)-sqrt(5))+1/(sqrt(5)-2)=5

Prove that: 1/(3-sqrt(8))-1/(sqrt(8)-\ sqrt(7))+1/(sqrt(7)-\ sqrt(6))-1/(sqrt(6)-\ sqrt(5))+1/(sqrt(5)-2)=5

Which is greater sqrt(11)-sqrt(6) or sqrt(17)-sqrt(12) ?