Nested radical

In <a href="/facts/Algebra/nMdqczjo">algebra</a>, a nested radical is a <a href="/facts/Radical_expression/XrRjtJGe">radical expression</a> (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression. Examples include

 
 
 
 
 
 5
 −
 2
 
 
 5
 
 
  
 
 
 ,
 
 
 {\displaystyle {\sqrt {5-2{\sqrt {5}}\ }},}

which arises in discussing the <a href="/facts/Pentagon/jeHEARHH">regular pentagon</a>, and more complicated ones such as

 
 
 
 
 
 
 2
 +
 
 
 3
 
 
 +
 
 
 4
 
 3
 
 
 
  
 
 
 3
 
 
 
 .
 
 
 {\displaystyle {\sqrt[{3}]{2+{\sqrt {3}}+{\sqrt[{3}]{4}}\ }}.}

Nested radical open-in-new

Nested radical