`sqrt(4+2sqrt(3))+sqrt(4-2sqrt(3))=?`

(sqrt(7)+2sqrt(3))(sqrt(7)-2sqrt(3))

Find the values of a and b in each of the following : (a)(5+2sqrt3)/(7+4sqrt(3))=a-6sqrt(3)" "(b)(3-sqrt(5))/(3+2sqrt(5))=asqrt(5)-(19)/(11) (c )(sqrt(2)+sqrt(3))/(3sqrt2-2sqrt(3))=2-bsqrt(6)" "(d)(7+sqrt(5))/(7-sqrt(5))-(7-sqrt(5))/(7+sqrt(5))=a+(7)/(11)sqrt(5b)

The value of (log)_(sqrt(4+2sqrt(2))sqrt(4-2sqrt(2)))2^9 is...........

Evaluate/simplify the following: |sqrt(7-4sqrt(3))|+|sqrt((2-sqrt(3))^2)|

Show that : (3sqrt(2)-2sqrt(3))/(3sqrt(2)+2sqrt(3))+(2sqrt(3))/(sqrt(3)-sqrt(2))=11

([(sqrt(2)+isqrt(3))+(sqrt(2)-isqrt(3))])/([(sqrt(3)+1sqrt(2))+(sqrt(3)-1sqrt(2))])

(1)/(2sqrt(5)-sqrt(3))-(2sqrt(5)+sqrt(3))/(2sqrt(5)+sqrt(3)) =

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))

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)

Prove that, cot 7 1/2 ^@ or tan 82 1/2 ^@ = (sqrt(3)+sqrt(2))(sqrt(2)+1) or sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)