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Square root
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Find the approximate value
Answer
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$\sqrt{ 108 }$
$6 \sqrt{ 3 }$
Find the square root
$\sqrt{ \color{#FF6800}{ 108 } }$
$ $ Do a factorization in prime factors for the integral number inside the radical sign $ $
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 3 } } }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 3 } } }$
$ $ Separate the part that can be taken out from the radical sign and the part that cannot be taken out $ $
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \times \color{#FF6800}{ 3 } ^ { 1 } }$
$ $ Separate the part that can be taken out of radical sign to different radical sign from the prime factor to the prime factor $ $
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ \color{#FF6800}{ 3 } ^ { 1 } }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 3 ^ { 2 } } \sqrt{ 3 ^ { 1 } }$
$ $ Get rid of the radical sign and change it to the denominator of the exponent $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \sqrt{ 3 ^ { 2 } } \sqrt{ 3 ^ { 1 } }$
$2 ^ { \frac { 2 } { 2 } } \sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 3 ^ { 1 } }$
$ $ Get rid of the radical sign and change it to the denominator of the exponent $ $
$2 ^ { \frac { 2 } { 2 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \sqrt{ 3 ^ { 1 } }$
$2 ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \times 3 ^ { \frac { 2 } { 2 } } \sqrt{ 3 ^ { 1 } }$
$ $ Reduce the fraction to the lowest term $ $
$2 ^ { \color{#FF6800}{ 1 } } \times 3 ^ { \frac { 2 } { 2 } } \sqrt{ 3 ^ { 1 } }$
$2 ^ { 1 } \times 3 ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \sqrt{ 3 ^ { 1 } }$
$ $ Reduce the fraction to the lowest term $ $
$2 ^ { 1 } \times 3 ^ { \color{#FF6800}{ 1 } } \sqrt{ 3 ^ { 1 } }$
$2 ^ { \color{#FF6800}{ 1 } } \times 3 ^ { 1 } \sqrt{ 3 ^ { 1 } }$
$ $ If the exponent is 1, get rid of it as it is unnecessary $ $
$2 \times 3 ^ { 1 } \sqrt{ 3 ^ { 1 } }$
$2 \times 3 ^ { \color{#FF6800}{ 1 } } \sqrt{ 3 ^ { 1 } }$
$ $ If the exponent is 1, get rid of it as it is unnecessary $ $
$2 \times 3 \sqrt{ 3 ^ { 1 } }$
$2 \times 3 \sqrt{ 3 ^ { \color{#FF6800}{ 1 } } }$
$ $ If the exponent is 1, get rid of it as it is unnecessary $ $
$2 \times 3 \sqrt{ 3 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ 3 } }$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 3 } }$
$\approx 10.3923$
Find the approximate value
$\sqrt{ \color{#FF6800}{ 108 } }$
$ $ Find the approximate value of the square root $ $
$\approx \color{#FF6800}{ 10.3923 }$
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