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Square root  Find the approximate value $\sqrt{ 275 }$
$5 \sqrt{ 11 }$
Find the square root
$\sqrt{ \color{#FF6800}{ 275 } }$
 Do a factorization in prime factors for the integral number inside the radical sign 
$\sqrt{ \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 11 } }$
$\sqrt{ \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \times 11 }$
 Separate the part that can be taken out of radical sign to different radical sign from the prime factor to the prime factor 
$\sqrt{ \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 11 }$
$\sqrt{ \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 11 }$
 Get rid of the radical sign and change it to the denominator of the exponent 
$\color{#FF6800}{ 5 } ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \sqrt{ 11 }$
$5 ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \sqrt{ 11 }$
 Reduce the fraction to the lowest term 
$5 ^ { \color{#FF6800}{ 1 } } \sqrt{ 11 }$
$5 ^ { \color{#FF6800}{ 1 } } \sqrt{ 11 }$
 If the exponent is 1, get rid of it as it is unnecessary 
$5 \sqrt{ 11 }$
$\approx 16.5831$
Find the approximate value
$\sqrt{ \color{#FF6800}{ 275 } }$
 Find the approximate value of the square root 
$\approx \color{#FF6800}{ 16.5831 }$
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