Theory:

Let us remember the formulas for solving and simplifying the radicals of positive integers \(m\), \(n\) and positive rational numbers \(a\) and \(b\).
 
The laws of radicals are:
 
S. NoRadical notationIndex notation
\(1\)ann=aa1nn=a
\(2\)an×bn=abna1n×b1n=ab1n
\(3\)anm=amn=amna1n1m=a1mn=a1m1n
\(4\)anbn=abna1nb1n=ab1n
Example:
Write the surd \(\sqrt{96}\) in its simplest form.
 
Solution:
 
\(\sqrt{96} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 3}\)
 
\(= \sqrt{2^2 \times 2^2 \times 2 \times 3}\)
 
\(= \sqrt{2^2} \times \sqrt{2^2} \times \sqrt{2} \times \sqrt{3}\) (Law of radicals (\(2\)))
 
\(= 2 \times 2 \times \sqrt{2} \times \sqrt{3}\) (Law of radicals (\(1\)))
 
\(= 4 \times \sqrt{2} \times \sqrt{3}\)
 
Therefore, the simplest form is \(4 \times \sqrt{2} \times \sqrt{3}\).