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Formula
Square root
$$\sqrt{ 675 }$$
$15 \sqrt{ 3 }$
Find the square root
$\sqrt{ \color{#FF6800}{ 675 } }$
 Do a factorization in prime factors for the integral number inside the radical sign 
$\sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } }$
$\sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } }$
 Separate the part that can be taken out from the radical sign and the part that cannot be taken out 
$\sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } }$
$\sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \times \color{#FF6800}{ 3 } ^ { 1 } }$
 Separate the part that can be taken out of radical sign to different radical sign from the prime factor to the prime factor 
$\sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ \color{#FF6800}{ 3 } ^ { 1 } }$
$\sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 5 ^ { 2 } } \sqrt{ 3 ^ { 1 } }$
 Get rid of the radical sign and change it to the denominator of the exponent 
$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ \frac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 2 } } } } \sqrt{ 5 ^ { 2 } } \sqrt{ 3 ^ { 1 } }$
$3 ^ { \frac { 2 } { 2 } } \sqrt{ \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 3 ^ { 1 } }$
 Get rid of the radical sign and change it to the denominator of the exponent 
$3 ^ { \frac { 2 } { 2 } } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ \frac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 2 } } } } \sqrt{ 3 ^ { 1 } }$
$3 ^ { \color{#FF6800}{ \frac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 2 } } } } \times 5 ^ { \frac { 2 } { 2 } } \sqrt{ 3 ^ { 1 } }$
 Reduce the fraction to the lowest term 
$3 ^ { \color{#FF6800}{ 1 } } \times 5 ^ { \frac { 2 } { 2 } } \sqrt{ 3 ^ { 1 } }$
$3 ^ { 1 } \times 5 ^ { \color{#FF6800}{ \frac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 2 } } } } \sqrt{ 3 ^ { 1 } }$
 Reduce the fraction to the lowest term 
$3 ^ { 1 } \times 5 ^ { \color{#FF6800}{ 1 } } \sqrt{ 3 ^ { 1 } }$
$3 ^ { \color{#FF6800}{ 1 } } \times 5 ^ { 1 } \sqrt{ 3 ^ { 1 } }$
 If the exponent is 1, get rid of it as it is unnecessary 
$3 \times 5 ^ { 1 } \sqrt{ 3 ^ { 1 } }$
$3 \times 5 ^ { \color{#FF6800}{ 1 } } \sqrt{ 3 ^ { 1 } }$
 If the exponent is 1, get rid of it as it is unnecessary 
$3 \times 5 \sqrt{ 3 ^ { 1 } }$
$3 \times 5 \sqrt{ 3 ^ { \color{#FF6800}{ 1 } } }$
 If the exponent is 1, get rid of it as it is unnecessary 
$3 \times 5 \sqrt{ 3 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } }$
 Simplify the expression 
$\color{#FF6800}{ 15 } \sqrt{ \color{#FF6800}{ 3 } }$
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