Class 8 Exam > Class 8 Videos > Examples: Square Roots
Examples: Square Roots Video Lecture - Class 8
FAQs on Examples: Square Roots Video Lecture - Class 8
| 1. What is a square root? |  |
Ans. A square root is a mathematical operation that, when applied to a number, gives another number as a result. The square root of a number is a value that, when multiplied by itself, gives the original number.
| 2. How do you find the square root of a number? | |
Ans. To find the square root of a number, you can use various methods such as the prime factorization method, long division method, or using a calculator. The most common method is using a calculator, where you input the number and press the square root button to get the result.
| 3. Can all numbers have square roots? | |
Ans. No, not all numbers have square roots. Non-negative numbers have square roots, but negative numbers do not have real square roots. However, complex numbers can have square roots, which involve the use of imaginary numbers.
| 4. What are the properties of square roots? | |
Ans. Some of the properties of square roots include:
1. The square root of a positive number is always positive.
2. The square root of zero is zero.
3. The square root of a negative number is not a real number.
4. The square root of a product is equal to the product of the square roots of the individual numbers.
5. The square root of a quotient is equal to the quotient of the square roots of the individual numbers.
| 5. How can square roots be used in real-life applications? | |
Ans. Square roots have various applications in real life, including:
1. Construction: Square roots are used to calculate diagonal measurements, ensuring accuracy in construction projects.
2. Finance: Square roots are used in financial calculations, such as calculating interest rates or risk assessments.
3. Physics: Square roots are used in physics equations to determine distances, velocities, and accelerations.
4. Engineering: Square roots are used in engineering calculations, such as determining electrical currents or signal processing.
5. Computer graphics: Square roots are used in computer graphics algorithms to calculate distances and angles for 3D rendering.
Text Transcript from Video
hello friends this video on questions
where you spot 19 is brought to you by
example.com know how to your um exam
question number one for the number two
six four five find the smallest whole
number by which it should be divided so
I should get a perfect square also find
the square root of the square okay first
let's try to see whether to search for
five is a perfect square or not so for
that what we would do we will do its
prime factorization so when you do it
fine rationalization with the smallest
prime number that divides it completely
is five so files into five twenty nine
six two six four five then the next
smallest prime number would be 23 so
twenty three into twenty three is five
twenty nine and then twenty three into
100 so this can be written as 2 6 4 5 is
equal to 5 into twenty three into twenty
three so you can find 2 does not exist
in tail but 23 exist in pairs so we can
write it as 5 into 23 square so now what
do you see do you think that 2645 is a
perfect square
no it is not because you cannot write it
as square of a single number because
files exist singly so then what should
we do what can we do to get a perfect
square numbers because the question
asked what is the smallest whole number
by which it should be divided so as to
make a perfect square so what are the
extracting because of digit is not a
perfect square by lisbeth expressing so
if we divide it by 5 then 5 + 5 will be
cancel out so this will become a perfect
square therefore it should be divided by
five now what happens if you divide it
by 5 so the moment you divide it by 5 it
becomes 23 square right so 23 square is
equal to how much this would be equal to
529 so therefore root over 5
9 is equal to 23 so this 23 is the
square root of the new square the new
square is $5.99 question number 2 the
students of class 8 of a school donated
rupees 2400 months in all 4 Prime
Minister's National Relief Fund each
student donated as many rupees as the
number of students in the class find the
number of students in the class so we do
not know the number of students in the
gas we also do not know how much money
each of them donated but we know that
the amount that each donated is equal to
the total number of students in the
class so let us assume that total number
of students in the class is equal to X
so if total number of students is X then
the donation per student is how much the
donation per student is also equal to X
so that is also 2 please X so what would
be the total donation the total donation
that gets collected will be equal to 2
please X into X X use each student
donation multiplied by the number of
students who donated but according to
the question the total donation is
repeat to 4 0 1 2 basically X into H is
equal to 2 4 0 1 so X into X would be x
squared is equal to 2 4 0 1 so what
would be the value of x it will be equal
to square root of 2 folded over so how
do we find the square root so for that
we will do prime factorization so it
gets divided by 7 7 into 343 then again
7 into 49 then again
seven so therefore two four zero one can
be written as seven into 7 into seven
into seventh that is equal to seven
squared into seven squared which is
equal to seven into seven square so two
four zero one is equal to 49 Incred
therefore root over 2 4 0 1 is equal to
49 so therefore there are 49 students in
the class question number three find the
smallest square number that is divisible
by each of the numbers 4 9 and 10 so a
number that is divisible by each of
these numbers what what would that
number be so that number will be a
multiple of each of these numbers so
basically that number will be a common
multiple of 4 9 9 10 so you want the
smallest number so basically we need to
calculate the least common multiple of 4
9 and 10 that is mvgame of 4 9 and 10 so
how do we find LCM again we have learned
all of this you want to revise go back
to the mathematics videos of class
fiction so this will get divided by 2
this is 5 10 again 202 to design this is
5 then 5 and then 9 so the LTM will be
equal to 2 into 2 into 5 into 9 that is
equal to 180 so 180 is the least common
multiple but the question is the
question asks us to find out the
smallest where Apple that is divisible
by all of these so we know that this is
the smallest number which is divisible
by all of these but is this a square
number so is 1 L 0 180
a square number which is about this
square so that is something you have to
find out so let us try to find its
square root now you prime factorize it
so this is 2 into 92 into 45 3 into 15 3
5 to 15 so there so one of L P can be
written as 2 into 2 into 3 into 3 into 5
so this can be written as 2 square into
3 square into fights so is this a
perfect square
no this is not a perfect way so what
should you do to get the nearest perfect
square octave so in order to get the
nearest perfect square let us multiply
this by 5 because 5 is that extra part
because of this this is not a square
number so so now we have two conditions
we have to make it a perfect square and
we also need to make that number is
divisible by 4 9 and 10 so therefore the
multiplying by 5 so what happens this
becomes 150 in two sides that is 2
square into 3 square into v square so
this actually becomes 2 into 3 into 5
whole square that is 30 whole square
which is equal to 900 therefore 900 is
the smallest square number that is
divisible by 4 9th and 10th question of
a phone for the number 768 find this one
whole number by this it should be
multiplied so as to get a perfect square
number okay so let's first factorize 758
the 2 into 3 84 then 292 into 19 into 2
so this is my 90 to the nine 8 to 9 to
18 to 6 is 12 to 4 the 8 to 8 is 16 2 to
the 4 2008 2 1 0 2 to the 4 to 6 to 12 2
3 6 so therefore 768 can be written as
into 2 into 2 into 2 into 2 into 2 into
2 into 2 8 times 2 into 3 so now you put
the tools in pairs so this becomes 2
square into 2 squared into 2 square into
2 square into 3 so this please are extra
parts because of this 750 angels akka
for the Nagas square number so what is
that number by this it should be
multiplied so it will be multiplied it
by 3 then what will happen this screen
will also become frequent to the effort
it will become a perfect clip therefore
it should be multiplied by 3 so when you
multiply it by 3 it becomes 2 into 2
into 2 into 2 into 3 square that is
equal to 2 to the fourth go to the 8
into the 1616 teaser 48 so 48 whole
square is equal to this side it will be
768 into 3 which is equal to 2 3 0 4 so
therefore we can take square root of 2 3
0 4 is equal to 48 so now this method
that is the prime factorization method
looks quite suitable to find out where
but again this method also become
sometimes very difficult when we are
dealing with larger numbers so therefore
we have another option that is option 3
which is called the division method to
find out square so in order to
understand the division method before
that we need to get some idea about this
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
where you spot 19 is brought to you by
example.com know how to your um exam
question number one for the number two
six four five find the smallest whole
number by which it should be divided so
I should get a perfect square also find
the square root of the square okay first
let's try to see whether to search for
five is a perfect square or not so for
that what we would do we will do its
prime factorization so when you do it
fine rationalization with the smallest
prime number that divides it completely
is five so files into five twenty nine
six two six four five then the next
smallest prime number would be 23 so
twenty three into twenty three is five
twenty nine and then twenty three into
100 so this can be written as 2 6 4 5 is
equal to 5 into twenty three into twenty
three so you can find 2 does not exist
in tail but 23 exist in pairs so we can
write it as 5 into 23 square so now what
do you see do you think that 2645 is a
perfect square
no it is not because you cannot write it
as square of a single number because
files exist singly so then what should
we do what can we do to get a perfect
square numbers because the question
asked what is the smallest whole number
by which it should be divided so as to
make a perfect square so what are the
extracting because of digit is not a
perfect square by lisbeth expressing so
if we divide it by 5 then 5 + 5 will be
cancel out so this will become a perfect
square therefore it should be divided by
five now what happens if you divide it
by 5 so the moment you divide it by 5 it
becomes 23 square right so 23 square is
equal to how much this would be equal to
529 so therefore root over 5
9 is equal to 23 so this 23 is the
square root of the new square the new
square is $5.99 question number 2 the
students of class 8 of a school donated
rupees 2400 months in all 4 Prime
Minister's National Relief Fund each
student donated as many rupees as the
number of students in the class find the
number of students in the class so we do
not know the number of students in the
gas we also do not know how much money
each of them donated but we know that
the amount that each donated is equal to
the total number of students in the
class so let us assume that total number
of students in the class is equal to X
so if total number of students is X then
the donation per student is how much the
donation per student is also equal to X
so that is also 2 please X so what would
be the total donation the total donation
that gets collected will be equal to 2
please X into X X use each student
donation multiplied by the number of
students who donated but according to
the question the total donation is
repeat to 4 0 1 2 basically X into H is
equal to 2 4 0 1 so X into X would be x
squared is equal to 2 4 0 1 so what
would be the value of x it will be equal
to square root of 2 folded over so how
do we find the square root so for that
we will do prime factorization so it
gets divided by 7 7 into 343 then again
7 into 49 then again
seven so therefore two four zero one can
be written as seven into 7 into seven
into seventh that is equal to seven
squared into seven squared which is
equal to seven into seven square so two
four zero one is equal to 49 Incred
therefore root over 2 4 0 1 is equal to
49 so therefore there are 49 students in
the class question number three find the
smallest square number that is divisible
by each of the numbers 4 9 and 10 so a
number that is divisible by each of
these numbers what what would that
number be so that number will be a
multiple of each of these numbers so
basically that number will be a common
multiple of 4 9 9 10 so you want the
smallest number so basically we need to
calculate the least common multiple of 4
9 and 10 that is mvgame of 4 9 and 10 so
how do we find LCM again we have learned
all of this you want to revise go back
to the mathematics videos of class
fiction so this will get divided by 2
this is 5 10 again 202 to design this is
5 then 5 and then 9 so the LTM will be
equal to 2 into 2 into 5 into 9 that is
equal to 180 so 180 is the least common
multiple but the question is the
question asks us to find out the
smallest where Apple that is divisible
by all of these so we know that this is
the smallest number which is divisible
by all of these but is this a square
number so is 1 L 0 180
a square number which is about this
square so that is something you have to
find out so let us try to find its
square root now you prime factorize it
so this is 2 into 92 into 45 3 into 15 3
5 to 15 so there so one of L P can be
written as 2 into 2 into 3 into 3 into 5
so this can be written as 2 square into
3 square into fights so is this a
perfect square
no this is not a perfect way so what
should you do to get the nearest perfect
square octave so in order to get the
nearest perfect square let us multiply
this by 5 because 5 is that extra part
because of this this is not a square
number so so now we have two conditions
we have to make it a perfect square and
we also need to make that number is
divisible by 4 9 and 10 so therefore the
multiplying by 5 so what happens this
becomes 150 in two sides that is 2
square into 3 square into v square so
this actually becomes 2 into 3 into 5
whole square that is 30 whole square
which is equal to 900 therefore 900 is
the smallest square number that is
divisible by 4 9th and 10th question of
a phone for the number 768 find this one
whole number by this it should be
multiplied so as to get a perfect square
number okay so let's first factorize 758
the 2 into 3 84 then 292 into 19 into 2
so this is my 90 to the nine 8 to 9 to
18 to 6 is 12 to 4 the 8 to 8 is 16 2 to
the 4 2008 2 1 0 2 to the 4 to 6 to 12 2
3 6 so therefore 768 can be written as
into 2 into 2 into 2 into 2 into 2 into
2 into 2 8 times 2 into 3 so now you put
the tools in pairs so this becomes 2
square into 2 squared into 2 square into
2 square into 3 so this please are extra
parts because of this 750 angels akka
for the Nagas square number so what is
that number by this it should be
multiplied so it will be multiplied it
by 3 then what will happen this screen
will also become frequent to the effort
it will become a perfect clip therefore
it should be multiplied by 3 so when you
multiply it by 3 it becomes 2 into 2
into 2 into 2 into 3 square that is
equal to 2 to the fourth go to the 8
into the 1616 teaser 48 so 48 whole
square is equal to this side it will be
768 into 3 which is equal to 2 3 0 4 so
therefore we can take square root of 2 3
0 4 is equal to 48 so now this method
that is the prime factorization method
looks quite suitable to find out where
but again this method also become
sometimes very difficult when we are
dealing with larger numbers so therefore
we have another option that is option 3
which is called the division method to
find out square so in order to
understand the division method before
that we need to get some idea about this
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
About this Video
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Oct 21, 2025
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