Question

find the square root of (2-root5) in the form of root a - root b ​

Answer 1

Given : 2  -  √5  

To find  :  square root    in the form of root a - root b ​

Solution:

Let say  

√a   -  √b    is the Square root   of   2  -  √5  

=> (√a   -  √b  )²   =  2  - √5

=> a  +  b  - 2√ab   = 2  - √5

=> a +  b   = 2      

2√ab = √5

=> 4ab = 5

=> ab = 5/4

Hence a & b are roots of Equation

x²  - 2x  +  5/4  = 0

=> x  =  (2  ± √(4  - 5) )/2

=> x  = ( 2   ±   i)/2

a =  ( 2  +   i)/2    ,  b =  ( 2  -   i)/2

Square root   of   2  -  √5       =   √ (( 2  +   i)/2 )   -  √ (( 2  -   i)/2 )

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