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Square root
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$\sqrt{ 225 }$
$15$
Find the square root
$\sqrt{ \color{#FF6800}{ 225 } }$
$ $ Do a factorization in prime factors for the integral number inside the radical sign $ $
$\sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } }$
$\sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } }$
$ $ Separate the part that can be taken out of radical sign to different radical sign from the prime factor to the prime factor $ $
$\sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } }$
$\sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 5 ^ { 2 } }$
$ $ Get rid of the radical sign and change it to the denominator of the exponent $ $
$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \sqrt{ 5 ^ { 2 } }$
$3 ^ { \frac { 2 } { 2 } } \sqrt{ \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } }$
$ $ Get rid of the radical sign and change it to the denominator of the exponent $ $
$3 ^ { \frac { 2 } { 2 } } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ \frac { 2 } { 2 } } }$
$3 ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \times 5 ^ { \frac { 2 } { 2 } }$
$ $ Reduce the fraction to the lowest term $ $
$3 ^ { \color{#FF6800}{ 1 } } \times 5 ^ { \frac { 2 } { 2 } }$
$3 ^ { 1 } \times 5 ^ { \color{#FF6800}{ \frac { 2 } { 2 } } }$
$ $ Reduce the fraction to the lowest term $ $
$3 ^ { 1 } \times 5 ^ { \color{#FF6800}{ 1 } }$
$3 ^ { \color{#FF6800}{ 1 } } \times 5 ^ { 1 }$
$ $ If the exponent is 1, get rid of it as it is unnecessary $ $
$3 \times 5 ^ { 1 }$
$3 \times 5 ^ { \color{#FF6800}{ 1 } }$
$ $ If the exponent is 1, get rid of it as it is unnecessary $ $
$3 \times 5$
$\color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 }$
$ $ Multiply $ 3 $ and $ 5$
$\color{#FF6800}{ 15 }$
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