7 7*(√(2+√3)) 7*(√(2+√3)) 7*(√(2+√3))*(2-√3)
----------- = ------------------------ = -------------------- = ------------------------- =
√(2+√3) √(2+√3)*√(2+√3) 2+√3 (2+√3)(2-√3)
7*(√(2+√3))*(2-√3)
= ----------------------------- = 7*(√(2+√3))*(2-√3) = 7*√(2+√3)*(2-√3)²) =
2²-√3²
=7*√((2²-√3²)*(2-√3)) =7*√((4-3) *(2+√3)) =7*√(2-√3))
1 1*(⁴√7- ⁴√2) ⁴√7-⁴√2 (⁴√7- ⁴√2 )
------------- = ------------------------------- = --------------- = ---------------- =
⁴√7+⁴√2 (⁴√7+ ⁴√2 )*(⁴√7-⁴√2 ) ⁴√7² -⁴√2² √7 -√2
( ⁴√7 -⁴√2)*(√7 +√2) ( ⁴√7 -⁴√2)*(√7 +√2) ( ⁴√7 -⁴√2)*(√7 +√2)
= ------------------------------- = ----------------------------- = ------------------------------
(√7 -√2 )(√7 +√2 ) 7-2 5
1 1*(√2-∛3) (√2-∛3) (√2-∛3)*(2²+2∛9+∛9²)
----------- = ------------------------ = ------------- = ------------------------------ =
√2+∛3 (√2+∛3)(√2-∛3) 2-∛9 (2-∛9)(2²+2∛9+∛9²)
(√2-∛3)*(4+2∛9+∛81) (√2-∛3)*(4+2∛9+∛81)
= ------------------------------- = ------------------------------- =- (√2-∛3)*(4+2∛9+∛81)
2³-∛9³ 8-9
1 1*((3+√2)+ √3) ((3+√2)+ √3)
----------------- = ------------------------------------- = ---------------------- =
3+√2- √3 ((3+√2)- √3)*((3+√2)+ √3) ((3+√2)²- √3²)
((3+√2)+ √3) ((3+√2)+ √3) ((3+√2)+ √3)
= -------------------------- = -------------------- = -------------------- =
3²+6√2+√2²-3 9+6√2+2-3 8+6√2
((3+√2)+√3)*(8- 6√2) ((3+√2)+√3)*(8- 6√2) ((3+√2)+√3)*(8- 6√2)
= ---------------------------------- = ------------------------------ = ----------------------------------
(8+6√2)*(8-6√2) 8²-(6√2)² 64-72
((3+√2)+√3)*(8- 6√2)
= - -------------------------------
12