" 2.Provethar "3-:2sqrt(5)" is irracional "

(i) sqrt(12+6sqrt(3))-sqrt(3) is (ii) sqrt((6-sqrt(5))+sqrt(14+6sqrt(5)))sqrt(3+2sqrt(2))-2sqrt(2)

(sqrt(5)-2)(sqrt(3)-sqrt(5))

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

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)

(sqrt(5)+sqrt(3))((3sqrt(3))/(sqrt(5)+sqrt(2))-sqrt(5)/(sqrt(3)+sqrt(2))) is equal to :

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

If p = (3-sqrt(5))/(3+sqrt(5)) and q = (3+sqrt5)/(3-sqrt(5)) ,find the value of p^(2) + q^(2) .