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Square root
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$12$
Find the square root
$\sqrt{ \color{#FF6800}{ 144 } }$
$ $ Do a factorization in prime factors for the integral number inside the radical sign $ $
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 4 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } }$
$ $ Separate the part that can be taken out of radical sign to different radical sign from the prime factor to the prime factor $ $
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 4 } } } \sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 4 } } } \sqrt{ 3 ^ { 2 } }$
$ $ Get rid of the radical sign and change it to the denominator of the exponent $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ \frac { \color{#FF6800}{ 4 } } { \color{#FF6800}{ 2 } } } } \sqrt{ 3 ^ { 2 } }$
$2 ^ { \frac { 4 } { 2 } } \sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } }$
$ $ Get rid of the radical sign and change it to the denominator of the exponent $ $
$2 ^ { \frac { 4 } { 2 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ \frac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 2 } } } }$
$2 ^ { \color{#FF6800}{ \frac { \color{#FF6800}{ 4 } } { \color{#FF6800}{ 2 } } } } \times 3 ^ { \frac { 2 } { 2 } }$
$ $ Reduce the fraction to the lowest term $ $
$2 ^ { \color{#FF6800}{ 2 } } \times 3 ^ { \frac { 2 } { 2 } }$
$2 ^ { 2 } \times 3 ^ { \color{#FF6800}{ \frac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 2 } } } }$
$ $ Reduce the fraction to the lowest term $ $
$2 ^ { 2 } \times 3 ^ { \color{#FF6800}{ 1 } }$
$2 ^ { 2 } \times 3 ^ { \color{#FF6800}{ 1 } }$
$ $ If the exponent is 1, get rid of it as it is unnecessary $ $
$2 ^ { 2 } \times 3$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \times 3$
$ $ Calculate power $ $
$\color{#FF6800}{ 4 } \times 3$
$\color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 }$
$ $ Multiply $ 4 $ and $ 3$
$\color{#FF6800}{ 12 }$
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