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Square root
$\sqrt[3]{ 216 }$
$6$
Find the square root
$\sqrt[ 3 ]{ \color{#FF6800}{ 216 } }$
 Do a factorization in prime factors for the integral number inside the radical sign 
$\sqrt[ 3 ]{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 3 } } }$
$\sqrt[ 3 ]{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 3 } } }$
 Separate the part that can be taken out of radical sign to different radical sign from the prime factor to the prime factor 
$\sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } } \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 3 } } }$
$\sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } } \sqrt[ 3 ]{ 3 ^ { 3 } }$
 Get rid of the radical sign and change it to the denominator of the exponent 
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ \frac { 3 } { 3 } } } \sqrt[ 3 ]{ 3 ^ { 3 } }$
$2 ^ { \frac { 3 } { 3 } } \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 3 } } }$
 Get rid of the radical sign and change it to the denominator of the exponent 
$2 ^ { \frac { 3 } { 3 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ \frac { 3 } { 3 } } }$
$2 ^ { \color{#FF6800}{ \frac { 3 } { 3 } } } \times 3 ^ { \frac { 3 } { 3 } }$
 Reduce the fraction to the lowest term 
$2 ^ { \color{#FF6800}{ 1 } } \times 3 ^ { \frac { 3 } { 3 } }$
$2 ^ { 1 } \times 3 ^ { \color{#FF6800}{ \frac { 3 } { 3 } } }$
 Reduce the fraction to the lowest term 
$2 ^ { 1 } \times 3 ^ { \color{#FF6800}{ 1 } }$
$2 ^ { \color{#FF6800}{ 1 } } \times 3 ^ { 1 }$
 If the exponent is 1, get rid of it as it is unnecessary 
$2 \times 3 ^ { 1 }$
$2 \times 3 ^ { \color{#FF6800}{ 1 } }$
 If the exponent is 1, get rid of it as it is unnecessary 
$2 \times 3$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 }$
 Multiply $2$ and $3$
$\color{#FF6800}{ 6 }$
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