Simplifying radicals without using prime factorization
Is there an easy way to simplify radicals?
For example, take the case of $sqrt{252}$. We can the find prime factorization of $252$ as $252=2times 2times 3 times 3times 7$ and thus we get $sqrt{252}=sqrt{2times 2times 3 times 3times 7}=6sqrt{7}.$
This method takes more time for large numbers. Without doing these calculations, i.e., without finding out prime factorization, is there any approach available to simplify radicals?
Please help. thanks.
elementary-number-theory prime-numbers prime-factorization
edited Nov 28 at 10:01
daniel
6,19322155
asked Nov 26 at 17:19
Kiran
3,2141633
add a comment |
Is there an easy way to simplify radicals?
For example, take the case of $sqrt{252}$. We can the find prime factorization of $252$ as $252=2times 2times 3 times 3times 7$ and thus we get $sqrt{252}=sqrt{2times 2times 3 times 3times 7}=6sqrt{7}.$
This method takes more time for large numbers. Without doing these calculations, i.e., without finding out prime factorization, is there any approach available to simplify radicals?
Please help. thanks.
elementary-number-theory prime-numbers prime-factorization
edited Nov 28 at 10:01
daniel
6,19322155
asked Nov 26 at 17:19
Kiran
3,2141633
For this kind of simplification, not really, I think. If all you're after is $15.87$, then there are numerous methods (not that I personally know very many, but I know they are there).
– Arthur
Nov 26 at 17:28
thanks for the info
– Kiran
Nov 26 at 17:34
1
If the number if definable as a multiple of some perfect square factors, that would mean the radical is reducible.For example:$252=16^2-2^2=(16-2)(16+2)=2^2.3^2.7$. I think this takes shorter time than factorizing.
– sirous
Nov 27 at 3:21
add a comment |
Is there an easy way to simplify radicals?
For example, take the case of $sqrt{252}$. We can the find prime factorization of $252$ as $252=2times 2times 3 times 3times 7$ and thus we get $sqrt{252}=sqrt{2times 2times 3 times 3times 7}=6sqrt{7}.$
This method takes more time for large numbers. Without doing these calculations, i.e., without finding out prime factorization, is there any approach available to simplify radicals?
Please help. thanks.
elementary-number-theory prime-numbers prime-factorization
edited Nov 28 at 10:01
daniel
6,19322155
asked Nov 26 at 17:19
Kiran
3,2141633
Is there an easy way to simplify radicals?
For example, take the case of $sqrt{252}$. We can the find prime factorization of $252$ as $252=2times 2times 3 times 3times 7$ and thus we get $sqrt{252}=sqrt{2times 2times 3 times 3times 7}=6sqrt{7}.$
This method takes more time for large numbers. Without doing these calculations, i.e., without finding out prime factorization, is there any approach available to simplify radicals?
Please help. thanks.
elementary-number-theory prime-numbers prime-factorization
elementary-number-theory prime-numbers prime-factorization
edited Nov 28 at 10:01
daniel
6,19322155
asked Nov 26 at 17:19
Kiran
3,2141633
edited Nov 28 at 10:01
daniel
6,19322155
asked Nov 26 at 17:19
Kiran
3,2141633
edited Nov 28 at 10:01
daniel
6,19322155
edited Nov 28 at 10:01
daniel
6,19322155
edited Nov 28 at 10:01
daniel
6,19322155
6,19322155
asked Nov 26 at 17:19
Kiran
3,2141633
asked Nov 26 at 17:19
Kiran
3,2141633
asked Nov 26 at 17:19
Kiran
3,2141633
3,2141633
For this kind of simplification, not really, I think. If all you're after is $15.87$, then there are numerous methods (not that I personally know very many, but I know they are there).
– Arthur
Nov 26 at 17:28
thanks for the info
– Kiran
Nov 26 at 17:34
1
If the number if definable as a multiple of some perfect square factors, that would mean the radical is reducible.For example:$252=16^2-2^2=(16-2)(16+2)=2^2.3^2.7$. I think this takes shorter time than factorizing.
– sirous
Nov 27 at 3:21
add a comment |
For this kind of simplification, not really, I think. If all you're after is $15.87$, then there are numerous methods (not that I personally know very many, but I know they are there).
– Arthur
Nov 26 at 17:28
thanks for the info
– Kiran
Nov 26 at 17:34
1
If the number if definable as a multiple of some perfect square factors, that would mean the radical is reducible.For example:$252=16^2-2^2=(16-2)(16+2)=2^2.3^2.7$. I think this takes shorter time than factorizing.
– sirous
Nov 27 at 3:21
For this kind of simplification, not really, I think. If all you're after is $15.87$, then there are numerous methods (not that I personally know very many, but I know they are there).
– Arthur
Nov 26 at 17:28
For this kind of simplification, not really, I think. If all you're after is $15.87$, then there are numerous methods (not that I personally know very many, but I know they are there).
– Arthur
Nov 26 at 17:28
thanks for the info
– Kiran
Nov 26 at 17:34
thanks for the info
– Kiran
Nov 26 at 17:34
1
1
If the number if definable as a multiple of some perfect square factors, that would mean the radical is reducible.For example:$252=16^2-2^2=(16-2)(16+2)=2^2.3^2.7$. I think this takes shorter time than factorizing.
– sirous
Nov 27 at 3:21
If the number if definable as a multiple of some perfect square factors, that would mean the radical is reducible.For example:$252=16^2-2^2=(16-2)(16+2)=2^2.3^2.7$. I think this takes shorter time than factorizing.
– sirous
Nov 27 at 3:21
add a comment |
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For this kind of simplification, not really, I think. If all you're after is $15.87$, then there are numerous methods (not that I personally know very many, but I know they are there).
– Arthur
Nov 26 at 17:28
thanks for the info
– Kiran
Nov 26 at 17:34
1
If the number if definable as a multiple of some perfect square factors, that would mean the radical is reducible.For example:$252=16^2-2^2=(16-2)(16+2)=2^2.3^2.7$. I think this takes shorter time than factorizing.
– sirous
Nov 27 at 3:21