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

Simplify: (i) (7+3\ sqrt(5))/(3+\ sqrt(5))-(7-3\ sqrt(5))/(3-\ sqrt(5)) (ii) 1/(2+sqrt(3)\ )+2/(sqrt(5)-\ sqrt(3))+1/(2-\ sqrt(5))

Simplify each of the following by removing radical signs and negative indices wherever they occur: (i)\ (sqrt(4))^(-3/4) (ii)\ (sqrt(5))^(-3)\ xx\ (sqrt(2))^(-3) (iii)1/(4^(-5)3)

Find x and y if: (3/sqrt(5) x-5)+i2 sqrt (5) y= sqrt(2)

The simplest rationalising factor of sqrt(3)+\ sqrt(5) is (a) sqrt(3)-5 (b) 3-sqrt(5) (c) sqrt(3)-sqrt(5) (d) sqrt(3)+\ sqrt(5)

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (a) (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

Factorise : 2sqrt(3)x^(2) + x - 5sqrt(3)

If angle between the line (x-2)/1=(y-3)/2=(z+5)/(-2) and 2x-y-kz=lambda is cos^-1 ((2sqrt2)/3) then find k (A) sqrt(3/5) (B) 3/sqrt5 (C) sqrt5/3 (D) sqrt(5/3)

Simplify the following expressions: (i) (4+sqrt(7))(3+sqrt(2)) (ii) (3+sqrt(3))(5-sqrt(2)) (iii) (sqrt(5)-2)(sqrt(3)-sqrt(5)) (iv) (sqrt(5)+sqrt(2))(sqrt(3)+sqrt(2))

Simplify the following expressions: (i)\ (4+\ sqrt(7))\ (3+sqrt(2)) (ii)\ (3+sqrt(3))\ (5-sqrt(2)) (iii)\ (sqrt(5)-2)\ (sqrt(3)-sqrt(5))

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