Thread: Surds please help

HELP!! i need help with these
Q1 Show that:
Ö2+1
----- = 3 +2Ö2
Ö2-1

Q2
Ö5-1
----- = 3+Ö5
Ö5-2

Q3 express : in the form kÖ5
1 1
---- - ----
3Ö5 2Ö20

Multiply the first by (sqrt(2)+1)/(sqrt(2)+1) to get

(sqrt(2)+1)^2/((sqrt(2)-1)(sqrt(2)+1)) = (sqrt(2)+1)^2/(sqrt(2)^2-sqrt(2)+sqrt(2)-1) = (2+2sqrt(2)+1)/1 = 3+2sqrt(2)

The second and third go in exactly the same way.