`frac{(sqrt 5 + sqrt 3i)^2}{(sqrt 5)^2- (sqrt 3i)^2}`

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

Rationalize the denominator 1/(sqrt 3 - sqrt 2) - 2/(sqrt 5 - sqrt 3) + 3/(sqrt 5 - sqrt 2)

If x= ( sqrt5- sqrt3)/ ( sqrt5+ sqrt3) and y= ( sqrt5+ sqrt3)/( sqrt5- sqrt3) find the value of x^(2) + y ^(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

The value of |{:(sqrt(13 )+ sqrt(3), 2sqrt(5),sqrt(5)),(sqrt(15) + sqrt(26),5,sqrt(10)),(3 + sqrt(65), sqrt(15),5):}|

Simplify: (i) (3sqrt(2)-2sqrt(2))/(3sqrt(2)+\ 2sqrt(3))+(sqrt(12))/(sqrt(3)-\ sqrt(2)) (ii) (sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3))+(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3))

Simplify each of the following : (i) 3/(5-sqrt(3))+2/(5+sqrt(3)) (ii) (4+sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (iii) (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+2)/(sqrt(5)-2)

The simplest rationalising factor of 2sqrt(5)-sqrt(3) is (a) 2sqrt(5)+\ 3 (b) 2sqrt(5)+sqrt(3) (c) sqrt(5)+sqrt(3)\ \ (d) sqrt(5)-sqrt(3)

Express the following in the form a+bi (sqrt3 + 5i) (sqrt3 -5i)^(2) + (-4+ 5i)^(2)