`sqrt ((3)^2 +(frac{4}{sqrt2})^2+(frac{5}{sqrt2})^2)`

frac{1}{sqrt7-4} frac{1}{sqrt11-7}

solve the equations: frac{2}{sqrt x} + frac{3}{sqrt y} =2 and frac{4}{sqrt x} - frac{9}{sqrt y} =-1

If 4(x-sqrt2)^(2)+lambda(y-sqrt3)^(2)=45 and (x-sqrt2)^(2)-4(y-sqrt3)^(2)=5 cut orthogonally, then integral value of lambda is ________.

Simplify each of the following expressions: (i) (3+sqrt(3))(2+sqrt(2)) (ii) (3+sqrt(3))(3-sqrt(3)) (iii) (sqrt(5)+sqrt(2))^2 (iv) (sqrt(5)-sqrt(2))(sqrt(5)+sqrt(2))

Simplify the following expressions: (i) (3+sqrt(3))\ (3-sqrt(3)) (ii) (sqrt(5)-\ sqrt(2)\ )(sqrt(5)+sqrt(2))

(3+sqrt5)^2 xx (3-sqrt5)^2 = ?

Solve the equation: (4sqrt(cos x/2)-5-(sqrt(2))/2)^2+ sqrt(2)(4sqrt(cos x/2)-5-(sqrt(2))/2)-(cosx)/2=0

Simplify the following expressions: (i)\ (sqrt(3)+\ sqrt(7))^2 (ii)\ (sqrt(5)-sqrt(3))^2 (iii)\ (2sqrt(5)+3sqrt(2))^2

One vertex of an equilateral triangle is (2,2) and its centroid is (-2/sqrt3,2/sqrt3) then length of its side is (a) 4sqrt(2) (b) 4sqrt(3) (c) 3sqrt(2) (d) 5sqrt(2)

Factorise: (i) 4sqrt(3)x^(2) + 5x-2sqrt(3) (ii) 7sqrt(2)x^(2)-10x - 4sqrt(2)