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Formula
Square root
Answer
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Find the approximate value
Answer
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$\sqrt{ 840 }$
$2 \sqrt{ 210 }$
Find the square root
$\sqrt{ \color{#FF6800}{ 840 } }$
$ $ Do a factorization in prime factors for the integral number inside the radical sign $ $
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } }$
$ $ Separate the part that can be taken out from the radical sign and the part that cannot be taken out $ $
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \times \color{#FF6800}{ 2 } ^ { 1 } \times 3 \times 5 \times 7 }$
$ $ Separate the part that can be taken out of radical sign to different radical sign from the prime factor to the prime factor $ $
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ \color{#FF6800}{ 2 } ^ { 1 } \times 3 \times 5 \times 7 }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 2 ^ { 1 } \times 3 \times 5 \times 7 }$
$ $ Get rid of the radical sign and change it to the denominator of the exponent $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \sqrt{ 2 ^ { 1 } \times 3 \times 5 \times 7 }$
$2 ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \sqrt{ 2 ^ { 1 } \times 3 \times 5 \times 7 }$
$ $ Reduce the fraction to the lowest term $ $
$2 ^ { \color{#FF6800}{ 1 } } \sqrt{ 2 ^ { 1 } \times 3 \times 5 \times 7 }$
$2 ^ { \color{#FF6800}{ 1 } } \sqrt{ 2 ^ { 1 } \times 3 \times 5 \times 7 }$
$ $ If the exponent is 1, get rid of it as it is unnecessary $ $
$2 \sqrt{ 2 ^ { 1 } \times 3 \times 5 \times 7 }$
$2 \sqrt{ 2 ^ { \color{#FF6800}{ 1 } } \times 3 \times 5 \times 7 }$
$ $ If the exponent is 1, get rid of it as it is unnecessary $ $
$2 \sqrt{ 2 \times 3 \times 5 \times 7 }$
$2 \sqrt{ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } }$
$ $ Multiply the numbers $ $
$2 \sqrt{ \color{#FF6800}{ 210 } }$
$\approx 28.9828$
Find the approximate value
$\sqrt{ \color{#FF6800}{ 840 } }$
$ $ Find the approximate value of the square root $ $
$\approx \color{#FF6800}{ 28.9828 }$
Solution search results
search-thumbnail-MCF $D$ 
$-36o$ 
$\dfrac {840} {7}$
1st-6th grade
Other
search-thumbnail-$81\bar{840} $
1st-6th grade
Other
search-thumbnail-The rationalizing factor of \sqrt{23} is 
$°$ $Options^{°}$ $0$ 
A 24 
23 
C \sqrt{23} 
D None of these
7th-9th grade
Other
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