Gabriel's idiocy.

Despitemy seemingly intact ego, sometimes I LOOK at myself  with self loathe, feeling guilty that such simple operations like radicalization of a fraction would fly over my head. I blame it on sleep deprivation, which is diminishing over time.

Reviewing some trigonometry, I stumbled upon this exercise on the excellent Free and Open Khan academy website.



 

                ___


Of course BC  is equal to 5 since tan is 1 and the other side(opposite to the angle) is 5.

However, it is not clear how

 5
___
√50


  1
____
  ___
√2


But the answer is: radicalization, i.e. multiplying the unit-length denominator by the monomial(term). In other words square root of 50 divided by square root of 50 multiplied by 5 divided by square root of 50.

Here are the steps:


0,70710678118654752440084436210485

 5
___
√50




Radicalization:

5·√50
____
50

Simplification:

 √50
 ____
  10

Factorization:

    ____
  √5· 10
  ______
    10
   
Square factorization:

     __    ___
   √5  · √10
   ___________
        10

Reverse radicalization:
       
    ___
   √5
   _____
    ___
   √10

Factorization

     ___
   √5
   _____
     ___
   √2·5

Square factorization:

     ___
   √5
   _____
     _      _
   √2 · √5

Finally:




   1
   ____
    ___
   √2

Which radicalized equates to: