Despitemy seemingly intact ego, sometimes

*I LOOK at m*

*yself*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: