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Formula
Square root
$$\sqrt{ 84 }$$
$2 \sqrt{ 21 }$
Find the square root
$\sqrt{ \color{#FF6800}{ 84 } }$
 Do a factorization in prime factors for the integral number inside the radical sign 
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \times 3 \times 7 }$
 Separate the part that can be taken out of radical sign to different radical sign from the prime factor to the prime factor 
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 3 \times 7 }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 3 \times 7 }$
 Get rid of the radical sign and change it to the denominator of the exponent 
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ \frac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 2 } } } } \sqrt{ 3 \times 7 }$
$2 ^ { \color{#FF6800}{ \frac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 2 } } } } \sqrt{ 3 \times 7 }$
 Reduce the fraction to the lowest term 
$2 ^ { \color{#FF6800}{ 1 } } \sqrt{ 3 \times 7 }$
$2 ^ { \color{#FF6800}{ 1 } } \sqrt{ 3 \times 7 }$
 If the exponent is 1, get rid of it as it is unnecessary 
$2 \sqrt{ 3 \times 7 }$
$2 \sqrt{ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } }$
 Multiply $3$ and $7$
$2 \sqrt{ \color{#FF6800}{ 21 } }$
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