CN4B_surds

## Surds

## Surd Algebra:

4sqrt(5) + 3sqrt(5) = 7sqrt(5)

8sqrt(3) * 2sqrt(3) = 16sqrt(3)sqrt(3) = 48

sqrt(8) / sqrt(2) = sqrt(4) = 2

sqrt(30) * sqrt(2) = sqrt(60)

sqrt(50) = sqrt(10)sqrt(5)

sqrt(2) * (sqrt(8) + sqrt(50)) = 2(sqrt(4) + sqrt(25)) = 2 * (2 + 5) = 14 :)
sqrt(2) * (sqrt(8) + sqrt(50)) = sqrt(2) * (2sqrt(2) + 5sqrt(2)) = sqrt(2) * 7sqrt(2) = 14

## Using conjugates:

(3 + sqrt(5))(3 - sqrt(5)) = 9 - 3sqrt(5) + 3sqrt(5) - sqrt(25) = 9 - sqrt(25) = 4

(5 - sqrt(2))(5 + sqrt(2)) = 25 - 2= 23
 
(9 + sqrt(100))(9 - sqrt(100)) = 81 - sqrt(10000) = -19 

(43 + sqrt(x))(43 - sqrt(x)) = 1849 -sqrt(x)^2 = 1849 - x

(x - sqrt(25))(x + sqrt(25)) = (x - 5)(x + 5) = x^2 - 25

## Rationalizing the denominator:

(sqrt(3) - 3)/(sqrt(5) - 6) = = =
                                                  
(sqrt(3) - 3)(sqrt(5) + 6)     sqrt(15) + 6sqrt(3) - 3sqrt(5) - 18
---------------------------  = ----------------------------------- = 
(sqrt(5) - 6)(sqrt(5) + 6)                 5 - 36
 
 // 1, 2, 3, 4,  5,  6,  7,  8,  9,  10,  11,  12  
 // 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 
                                                             
(sqrt(4) + 2)(sqrt(2) - 2)/(sqrt(2) + 2)(sqrt(2) - 2) = sqrt(8) - 2sqrt(4) + 2sqrt(2) - 4/(2 - 4) = 2sqrt(2) -4 +2sqrt(2) - 4 /-2 = 4sqrt(2) -8 / -2 = -2sqrt(2) + 4

(5 + sqrt(3))/(7 - sqrt(7)) = (5 + sqrt(3)(7 + sqrt(7)/(7 - sqrt(7)(7 + sqrt(7) = 35 + 5sqrt(7) + 7sqrt(3) + sqrt(21) / 42

Example Question from 2018 Exam (copy link into browser):
data:image/png;base64,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