Partial root extraction is not a complicated matter, and if you learn it correctly, it can be very helpful, for example, when working with fractions. An example might look like this:
Simplify the following fractionAt first glance, it seems that this fraction cannot be simplified further, but it can:
If we want to follow the rule that there should be no fraction in the denominator, we can rationalize the fraction:
It might seem complicated, but it is not. Once you understand a few basic principles, you will be able to handle similar examples on your own and without difficulties.
It is important to realize that 
is equal to 
, meaning that the product under the root is equal to the product of the individual terms under the root. Knowing this fact allows you to partially root fractions. We know that the square root of 4 is 2, so the previous example would look like:
In other words, you need to break down the number under the root into a product of two numbers. Test whether the root of the given number is an integer. If it is not, continue with this breakdown/testing until you reach the prime factorization.
Example
1) Partially root the following expression: 
2) Partially root the following expression: 
3) Partially root the following expression: 
4) Partially root the following expression: 
Finally, we should rationalize the fraction (see article Usměrňování zlomků)
na intervalu 
.