CBSE Class 8 > Class 8 Videos > Prime Factorization Method - Square and Square Roots, Mathematics, CBSE Class 8
Prime Factorization Method - Square and Square Roots, CBSE Class 8 Video
FAQs on Prime Factorization Method - Square and Square Roots, Mathematics, CBSE Class 8
| 1. What is the prime factorization method for finding square roots? |  |
Ans. The prime factorization method is a technique used to find the square root of a given number. In this method, we first express the given number as a product of its prime factors. Then, we group the prime factors in pairs and take one factor from each pair. The product of these factors gives us the square root of the given number.
| 2. How do you find the square root of a number using prime factorization method? | |
Ans. To find the square root of a number using the prime factorization method, follow these steps: 1. Express the given number as a product of its prime factors. 2. Group the prime factors in pairs. 3. Take one factor from each pair. 4. Multiply all the factors selected in step 3 to get the square root of the given number.
| 3. Can the prime factorization method be used to find the square root of any number? | |
Ans. Yes, the prime factorization method can be used to find the square root of any number. This method is particularly useful when dealing with large numbers, as it allows us to simplify the calculation by breaking down the number into its prime factors.
| 4. Are there any limitations or drawbacks to using the prime factorization method for finding square roots? | |
Ans. While the prime factorization method is a reliable technique for finding square roots, it can be time-consuming for very large numbers with numerous prime factors. Additionally, this method may not be suitable for finding the square root of irrational numbers, as they cannot be expressed as a product of prime factors.
| 5. How does the prime factorization method for finding square roots differ from other methods? | |
Ans. The prime factorization method differs from other methods, such as the long division method or the approximation method, by its focus on breaking down the given number into its prime factors. This approach allows for a systematic and precise calculation of the square root, ensuring accurate results. Other methods may involve estimation or more complex mathematical operations.
Text Transcript from Video
hello friends this video on smashing
schedules but 18 is brought to you by
examples or car no no to your calm exam
look at the second options that we have
and that is the prime factorization
method so I hope all of you remember
what is prime factorization if you are
given a number you can write that number
in terms of product of its prime factors
that is factors of number which are also
prime numbers so if you are providing
how to do kind factorization you can get
for the mathematics videos of plastic
okay so for now let's take an example
let's say that you have to find out
square root of hundred so we are taking
a simpler example to understand it for
now so our first step would be to prime
and factorize hundred so how do we do
can factorization by dividing it by the
smallest possible prime number such that
that prime number exactly divide this
number country so in this case that
smallest prime number would be 2 so 2
into 50 is hundred further again it
would be 2 so 2 into 25 it would be to
speak then it is not 2 not 3 because 3
doesn't divide verifies completely then
it would be 5 2 5 into 5 is 25 and then
5 into 1 so therefore you can say 100
can be written as 2 into 2 into 5 into 5
so 2 into 2 into 5 into 5 so how many
times we have 2 so 2 multiplied to
itself that is 2 square similarly sized
multiplied to Excel is 5 square so 2
square into v square is actually 2 into
5 whole square so 2 into 5 is 10 so we
see that 100 is equal to 10 square so
that means if I want to get hundred from
10 we square it so if we want to get 10
from hundred we will have to find the
square root the square root of
is equal to 10 so in this fashion we can
also find out where so looking at this
method itself you would have seen that
it is a more ordinary method and a
better method of course that is repeated
subtraction method so let us take one
more example so this time let's take a
bigger number let's say you have to find
out square root of seven thousand seven
hundred forty four so let's prime
factorize it seven seven four four so it
will get divided by two is two into
three eight seven - just seven seven
four four
then again 200 - to raise the 18 2 to
the 6 - 6 or 12 then 8 8 to 9 to 18 this
is the 12th 2016 then again 2 into 4 is
8 2 into 16 2008 again 2 to the 4 2 4
the 8 2 to the 4 200 2 to to the 4 - 1 2
- and then this one 21 is not divisible
by 2 3 4 5 6 7 8 9 10 but it'll be
usable 9/11 now once that cases you know
what you can do is then you have one at
the end so it is very obvious that it is
it is not divisible by 2 4 6 or 8 it is
also not divisible by 10 so you are left
with a few options that is 3/7 and 11 so
you try only those numbers Thanks so
that you do not waste a lot of time
so therefore looking at this you can say
that 7 7 4 toll is 2 into 2 into 2 into
2 into 2 into 2 so you have 6 times 2 &
2 times 11 so now you make pairs of T so
that it creates our job easier so a pair
of 2 is 2 squared again another pair of
tools a - squaring it one more pair of
two straight and then a pair of xi 2 xi
square so this can be written as 2 into
2
do into 11 Colquitt so therefore we can
say a root over 7 7 4 4 will be equal to
2 into 2 into 2 is 2 11 which is equal
to 88
so therefore square root of 7 7 4 4 is
equal to 88 so you see this is a more
convenient method to find out square
root of a number
[Music]
now this is the help of the Strand
factorization method you can even find
out whether a given number is a perfect
square or not so this is not away
because what might happen is you might
sometimes come across numbers for which
you are unable to find the square you
let me give you an example let's say
that you are given a number 220 and I
ask you to find out the square root of
220 so as per process you will do its
line factorization so 200 - 200 - 0 and
then 2 fives the same to try to change
511 255 so 220 can be written as 2 into
2 into 5 into 11 now when you look at
this you see that to a different tale so
you can write it as 2 square but why it
doesn't exist in there
similarly 11 doesn't exist in there so
therefore we are not able to write 220
as square of some numbers only when you
are able to write it n square of some
numbers only that means that 220 is a
perfect square but in this case we are
unable to write 220 and a square of a
single number
this shows that 220 is not a perfect
square
now if 220 is not a perfect square we
will never be able to get the square
root of complaining like you will not
get a whole number for square root of
220 so now if I ask you that is there
any way that you can find out the
nearest perfect square so okay we got it
that 220 is not the first
when so what do you think could be a
perfect square something years into 20
now to find out the perfect square one
option is you either divide two 20 by 5
into 11 because if you divide two 20 by
5 into 11 what will happen despite and
11 will vanish so you will be left with
2 to the power 2 it is 4 which is a
project where another option is you
multiply to 20 so there are two options
option 1 is divided to 20 by 5 into 11
if you divide 2 20 by 5 into 11
what will happen despite into 11 will
vanish and you will be left with 4 which
is the perfect square the second option
is you multiply to 20 by 5 into 11 in
that tip what will happen in that case
you will get two pilots ratified square
you will get to 11 that is Levin square
so in this case so when you do this the
220 number changes to 4 2 4 is a perfect
square and when you do this then the
number 220 changes to X what number it
becomes 2 20 into piles into 11 and this
number becomes equal to 2 squared into v
square into 11 square so this time you
are multiplying it with 5 by 11 so this
becomes 2 into 5 into 11 whole square
that is 110 whole square so if you
follow the second option you get 110
whole square which is a perfect square
if you follow the first option you get 2
squared it is 4 which is a perfect
square so therefore for non perfect when
you ever come across the situation where
you when you climb factorize a given
numbers you are not able to see that
number as a
we're a mobile number that means that
number is not a perfect way but if you
still want to get a perfect square from
that number then you either need to
multiply or divide that number with this
extra part of the number because in this
case this 220 is not a perfect coin
because of this extra part filing 211
this is the extra part which is not
allowing it to be a perfect square so
you either divide this number by the
extra pack or you multiply this number
by this extra part in that case this
becomes or the number gets converted
into a perfect square number
thank you please visit example.com for
free quality education you can learn
with a simple four-step learning process
wherein you can watch video lessons you
can ask your questions you can refer
notes and you can take a free online
test we have content for class 6 to 12
on physics chemistry mathematics and
biology along with practical videos so
please subscribe to our channel for
daily updates thank you
the question diamonds
schedules but 18 is brought to you by
examples or car no no to your calm exam
look at the second options that we have
and that is the prime factorization
method so I hope all of you remember
what is prime factorization if you are
given a number you can write that number
in terms of product of its prime factors
that is factors of number which are also
prime numbers so if you are providing
how to do kind factorization you can get
for the mathematics videos of plastic
okay so for now let's take an example
let's say that you have to find out
square root of hundred so we are taking
a simpler example to understand it for
now so our first step would be to prime
and factorize hundred so how do we do
can factorization by dividing it by the
smallest possible prime number such that
that prime number exactly divide this
number country so in this case that
smallest prime number would be 2 so 2
into 50 is hundred further again it
would be 2 so 2 into 25 it would be to
speak then it is not 2 not 3 because 3
doesn't divide verifies completely then
it would be 5 2 5 into 5 is 25 and then
5 into 1 so therefore you can say 100
can be written as 2 into 2 into 5 into 5
so 2 into 2 into 5 into 5 so how many
times we have 2 so 2 multiplied to
itself that is 2 square similarly sized
multiplied to Excel is 5 square so 2
square into v square is actually 2 into
5 whole square so 2 into 5 is 10 so we
see that 100 is equal to 10 square so
that means if I want to get hundred from
10 we square it so if we want to get 10
from hundred we will have to find the
square root the square root of
is equal to 10 so in this fashion we can
also find out where so looking at this
method itself you would have seen that
it is a more ordinary method and a
better method of course that is repeated
subtraction method so let us take one
more example so this time let's take a
bigger number let's say you have to find
out square root of seven thousand seven
hundred forty four so let's prime
factorize it seven seven four four so it
will get divided by two is two into
three eight seven - just seven seven
four four
then again 200 - to raise the 18 2 to
the 6 - 6 or 12 then 8 8 to 9 to 18 this
is the 12th 2016 then again 2 into 4 is
8 2 into 16 2008 again 2 to the 4 2 4
the 8 2 to the 4 200 2 to to the 4 - 1 2
- and then this one 21 is not divisible
by 2 3 4 5 6 7 8 9 10 but it'll be
usable 9/11 now once that cases you know
what you can do is then you have one at
the end so it is very obvious that it is
it is not divisible by 2 4 6 or 8 it is
also not divisible by 10 so you are left
with a few options that is 3/7 and 11 so
you try only those numbers Thanks so
that you do not waste a lot of time
so therefore looking at this you can say
that 7 7 4 toll is 2 into 2 into 2 into
2 into 2 into 2 so you have 6 times 2 &
2 times 11 so now you make pairs of T so
that it creates our job easier so a pair
of 2 is 2 squared again another pair of
tools a - squaring it one more pair of
two straight and then a pair of xi 2 xi
square so this can be written as 2 into
2
do into 11 Colquitt so therefore we can
say a root over 7 7 4 4 will be equal to
2 into 2 into 2 is 2 11 which is equal
to 88
so therefore square root of 7 7 4 4 is
equal to 88 so you see this is a more
convenient method to find out square
root of a number
[Music]
now this is the help of the Strand
factorization method you can even find
out whether a given number is a perfect
square or not so this is not away
because what might happen is you might
sometimes come across numbers for which
you are unable to find the square you
let me give you an example let's say
that you are given a number 220 and I
ask you to find out the square root of
220 so as per process you will do its
line factorization so 200 - 200 - 0 and
then 2 fives the same to try to change
511 255 so 220 can be written as 2 into
2 into 5 into 11 now when you look at
this you see that to a different tale so
you can write it as 2 square but why it
doesn't exist in there
similarly 11 doesn't exist in there so
therefore we are not able to write 220
as square of some numbers only when you
are able to write it n square of some
numbers only that means that 220 is a
perfect square but in this case we are
unable to write 220 and a square of a
single number
this shows that 220 is not a perfect
square
now if 220 is not a perfect square we
will never be able to get the square
root of complaining like you will not
get a whole number for square root of
220 so now if I ask you that is there
any way that you can find out the
nearest perfect square so okay we got it
that 220 is not the first
when so what do you think could be a
perfect square something years into 20
now to find out the perfect square one
option is you either divide two 20 by 5
into 11 because if you divide two 20 by
5 into 11 what will happen despite and
11 will vanish so you will be left with
2 to the power 2 it is 4 which is a
project where another option is you
multiply to 20 so there are two options
option 1 is divided to 20 by 5 into 11
if you divide 2 20 by 5 into 11
what will happen despite into 11 will
vanish and you will be left with 4 which
is the perfect square the second option
is you multiply to 20 by 5 into 11 in
that tip what will happen in that case
you will get two pilots ratified square
you will get to 11 that is Levin square
so in this case so when you do this the
220 number changes to 4 2 4 is a perfect
square and when you do this then the
number 220 changes to X what number it
becomes 2 20 into piles into 11 and this
number becomes equal to 2 squared into v
square into 11 square so this time you
are multiplying it with 5 by 11 so this
becomes 2 into 5 into 11 whole square
that is 110 whole square so if you
follow the second option you get 110
whole square which is a perfect square
if you follow the first option you get 2
squared it is 4 which is a perfect
square so therefore for non perfect when
you ever come across the situation where
you when you climb factorize a given
numbers you are not able to see that
number as a
we're a mobile number that means that
number is not a perfect way but if you
still want to get a perfect square from
that number then you either need to
multiply or divide that number with this
extra part of the number because in this
case this 220 is not a perfect coin
because of this extra part filing 211
this is the extra part which is not
allowing it to be a perfect square so
you either divide this number by the
extra pack or you multiply this number
by this extra part in that case this
becomes or the number gets converted
into a perfect square number
thank you please visit example.com for
free quality education you can learn
with a simple four-step learning process
wherein you can watch video lessons you
can ask your questions you can refer
notes and you can take a free online
test we have content for class 6 to 12
on physics chemistry mathematics and
biology along with practical videos so
please subscribe to our channel for
daily updates thank you
the question diamonds
About this Video
Apr 18, 2026 Last updated
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