Partially taking the root
With the help of root rules, it is possible to partially take roots. The root rule is applied backwards:
$\sqrt[n]{a\cdot b}=\sqrt[n]{a}\cdot\sqrt[n]{b}$
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Remember
When partially taking the root, the root is divided into takeable and nontakeable roots. Then the root is taken from the takeable while the nontakeable roots remain.
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Method
 Decomposition into prime numbers
 Summarize into factors with even exponents
 "Divide" the root (apply the root law backwards)
 Partially take roots
Example
$\sqrt{44}$

Decomposition into prime numbers
Divide the number into a product of primes.
$=\sqrt{2\cdot2\cdot11}$ 
Summarize into factors with even exponents
If possible, summarize in factors that have an even exponent.
$=\sqrt{2^2\cdot11}$ 
"Divide" the root
Divide the root by applying the multiplication law backwards. The result is a takeable and a nontakeable root.
$=\sqrt{2^2}\cdot\sqrt{11}$ 
Partially take roots
Take roots (from the takeable ones) by shortening the exponent and the root.
$=\sqrt[\color{red}{2}]{\color{blue}{2}^{\color{red}{2}}}\cdot\sqrt{11}=\color{blue}{2}\cdot\sqrt{11}$
$\sqrt{44}=2\sqrt{11}$