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Formula
Square root
Answer
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Find the approximate value
Answer
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$\sqrt{ 980 }$
$14 \sqrt{ 5 }$
Find the square root
$\sqrt{ \color{#FF6800}{ 980 } }$
$ $ Do a factorization in prime factors for the integral number inside the radical sign $ $
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ 2 } } }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ 2 } } }$
$ $ Separate the part that can be taken out from the radical sign and the part that cannot be taken out $ $
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \times \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ 2 } } \times 5 }$
$ $ Separate the part that can be taken out of radical sign to different radical sign from the prime factor to the prime factor $ $
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 5 }$
$\sqrt{ \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 7 ^ { 2 } } \sqrt{ 5 }$
$ $ Get rid of the radical sign and change it to the denominator of the exponent $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \sqrt{ 7 ^ { 2 } } \sqrt{ 5 }$
$2 ^ { \frac { 2 } { 2 } } \sqrt{ \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ 2 } } } \sqrt{ 5 }$
$ $ Get rid of the radical sign and change it to the denominator of the exponent $ $
$2 ^ { \frac { 2 } { 2 } } \times \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \sqrt{ 5 }$
$2 ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \times 7 ^ { \frac { 2 } { 2 } } \sqrt{ 5 }$
$ $ Reduce the fraction to the lowest term $ $
$2 ^ { \color{#FF6800}{ 1 } } \times 7 ^ { \frac { 2 } { 2 } } \sqrt{ 5 }$
$2 ^ { 1 } \times 7 ^ { \color{#FF6800}{ \frac { 2 } { 2 } } } \sqrt{ 5 }$
$ $ Reduce the fraction to the lowest term $ $
$2 ^ { 1 } \times 7 ^ { \color{#FF6800}{ 1 } } \sqrt{ 5 }$
$2 ^ { \color{#FF6800}{ 1 } } \times 7 ^ { 1 } \sqrt{ 5 }$
$ $ If the exponent is 1, get rid of it as it is unnecessary $ $
$2 \times 7 ^ { 1 } \sqrt{ 5 }$
$2 \times 7 ^ { \color{#FF6800}{ 1 } } \sqrt{ 5 }$
$ $ If the exponent is 1, get rid of it as it is unnecessary $ $
$2 \times 7 \sqrt{ 5 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } \sqrt{ \color{#FF6800}{ 5 } }$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 14 } \sqrt{ \color{#FF6800}{ 5 } }$
$\approx 31.305$
Find the approximate value
$\sqrt{ \color{#FF6800}{ 980 } }$
$ $ Find the approximate value of the square root $ $
$\approx \color{#FF6800}{ 31.305 }$
Solution search results
search-thumbnail-The rationalizing factor of \sqrt{23} is 
$°$ $Options^{°}$ $0$ 
A 24 
23 
C \sqrt{23} 
D None of these
7th-9th grade
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