Square Roots - Basics Video Lecture - Banking Exams

hello friends today we will discuss the
topic of square root now let us have
first of all an overview of the session
now in the session we will cover how to
calculate the square root of a number
then we will do the application of
square root in certain questions lastly
you will have some practice questions
with an answer key now let us first of
all friends find out how to calculate
the square root of a number now there
are two methods of finding the square
root one is called the division method
and the other one is called the
factorization method let us first of all
start with the division method
now let me first of all pick an example
here I have picked up a number s 289 now
then we have to find the root using
division method we start with the right
hand side of the number from here we
make pairs of two two digits and then we
separate the first pair or whatever is
the first single digit number in this
example I have two now the next step is
we will think of a number whose square
is immediately lesser than or equal to
the first number in the beginning of the
number now in my case I know that the
number is 1 1 square is 1 which is
immediately lesser than the number 2 now
we will write this number 1 here as
minus over here and so we'll write the
square over here now in the next step as
we do in division we will subtract the 2
now in the next step what we will do is
we will pick up the entire the earth and
bring it down so I pick up this entire
89 and bring this number down in the
next step French whatever number we have
over here with a twice this number and
write this number over here so I do
twice of 1 as 2 and place it over here
now in the next step friends what I have
to do is I'll pick up a digit leave that
pitch it over here and the same digit I
place over here
then I will multiply this entire
two-digit number with the digit which
are placed at the end of this number and
result in a product which is immediately
lesser than or equal to this number 189
so in this case that number is 7 and I
write the product over here then as we
proceed in simple division we take that
the friends and the remainder comes out
to be 0 and the division has ended
perfectly and then we can conclude that
the square root of 289 is 17 so I hope
friends you have understood this
division method
now let us now go to the second matter
that is called the factorization matter
now using this factors matter first of
all we need to find the prime factors of
a number whose square root we want to
evaluate now let me pick an example here
I have chosen the number as 36 now first
of all we will find the prime factors of
this number 36
now after we have found the prime
factors of the number 36 here I am
writing them in expanded form
now vine finding the root of 36 using
factorization method we will first of
all make pairs of the similar factors so
here I have made a bigger of 2 as well
as a pair of 3 now for every pair that
we have made while taking the root the
pickup's single factor so for a pair of
to have picked up a single 2 similarly
for a pair of 3 I have picked up a
single 3 I will multiply the 2 and hence
the result is 6 so the root of 36 is 6
so these are the 2 methods through which
we can find the square root of a number
now let us start with certain questions
here we go to the first question in this
question we have to find the square root
of this bigger number this we should to
using the division method but I'll teach
you one more trick which you can easily
apply in mcq based paper to find the
square root of such bigger numbers now
the trick is friends we should go to the
choices and in each choice we should
check only the unit's digit now if we
square the unit's digit then the result
should be 9 as in my given number but
for examples here we have units digit in
the first option as 2 2 squared is 4
hence first choice is not my answer
similarly if I squared the unit's digit
of the second choice I get the result as
5 whereas my number in the question ends
with 9
hence we can eliminate the second choice
also on the same grounds we can
eliminate the fourth option as it ends
with 6 and the square of 6 ends with 6
we are left fit now only the third
choice which will be my answer and also
for your verification you can check that
in the third choice the unit's digit is
3 and the square of 3 and so it's 9 so I
hope friends that this trick is very
useful to you in most of the aptitude
exams let us go to the next question now
in this question we have to find the
fruit of certain numbers again we should
use the division matter of finding the
roots but for smaller numbers such as
these it is suggested that you learn the
squares some vital 31 approximately so I
start writing the root of number 324
which is eating now in the next step we
will add the number 7 and the result is
25 now you can see friends there is a
root sign on the top of this much
expression so in the next step we will
do root of 25 and the result is 5 now if
we have salt till this much part of the
question
now in the next step
they'll pick up this number for ad with
the spice the result is nine and again
there is a root sign on the top of this
expression so we will do root of nine
the result is three then we pick up this
22 add with this three the result is 25
and then we take the root of 25
the result is five and in the last step
we add the number 116 the result comes
out to be 121 and in the last step we
have to take again the root of 121 hence
the result is 11 so I hope friends that
you have understood this question let us
move to the next question
now this is a similar question as a
previous one so we'll start taking the
root of 729 which comes out to be 27
then I'll take the root of 121 which is
11 and then 676 which is 26 now after we
have evaluated the square roots we find
that students that there is a similar
number in the numerator and similar
number in the denominator
which we can eliminate now saying that
we can eliminate this 11 and also we can
eliminate this 26 and hence the result
is 1 now this question becomes very easy
to solve if you have learnt all the
squares as I said initially now let's go
to the next question now in this
question friends I'll teach you one more
trick that is how to find the root of
the decimal numbers now very first step
is we must check that each of the
numbers should have even number of
decimal places
as in the first number there are 2
decimal places in the second there are
four in the third there are 6 and in the
fourth one there are 8 now by taking the
root what we do that if the number of
decimal places are even we find the root
of the number without using the decimal
now without using the decimal each of
the numbers is equal to the given number
in the question itself that is 18000 225
whose square root we are already given
as 135 so I will take the root of these
numbers without using the decimal which
I write for each number as 135 but
friends to find the root of the original
number what we do is click count the
number of decimal places in each number
and vive taking the root we shift the
decimal to
off of the number of places so when I
sell half that means in the given number
there were two decimal places I took
half of two titers one so I shifted the
decimal by one place and hence the exact
square root of this number becomes
thirteen point five so as I proceed with
the next I first of all take the root
without the decimal then I count the
number of decimal places which are four
take half of them and shift the decimal
position by two places towards the left
I did not mention it initially but first
we have to shift the decimal position
towards the left so exact root becomes
one point three five
so similarly if we do at the next number
we take the roots without the decimal
then count the decimal positions over
here which are six take half of them
that is three and shift the decimal
position by three places towards the
left
hence the root comes out to be zero
point bunkie five now same way if we
proceed with the next number take the
root as 135 without the decimal then
count the decimal positions over here
which are eight take half of them and
shift the decimal number by four places
towards the left and hence the root
becomes zero point zero one three five
finally you add all the numbers
and the researchers 14.99 eight sites
let's see the next question in this
question friends we need to find which
smallest number needs to be subtracted
or added to the given number so that it
becomes a perfect square in our face
when we have to find what needs to be
added or subtracted we always take the
root of the number using division method
which we had already discussed so here
I'll first of all take the root of
sixteen hundred and forty using the
division method now here I stopped
because the division has not terminated
completely instead we have found certain
remainder so in the first part of the
question friends then we have to answer
what needs to be subtracted we subtract
the remainder it says
because for the division to terminate
completely there should not be any
remainder and hence the number is 40 it
says which needs to be subtracted for
the number to be a perfect square but in
the second part of the question where we
have to find what needs to be added
there is one step that is different now
while taking the route we have picked up
the digits zero because we want to have
a product which is immediately lesser
than this 40 the instead of this steps
we will pick up the next higher digit
that is instead of placing zero at the
back of it we will place one which will
result in 81 multiply it with 1 and the
product that it divides now this product
has become higher than this number 40 we
subtract the 2
and we get the result as 41 so France 41
needs to be added to the original number
1640 to make it a perfect square of 41
so we add 41 with 16 140 so that it
becomes the square of 41 now let us go
to the next question now here we have to
find which smallest number needs to be
multiplied and divided it with a given
number that is 750 to make it a perfect
square now in contrast to the previous
question where we have discussed what
needs to be added or subtracted here we
have to find what needs to be multiplied
or divided we use the factorization
method of finding the root
hence we start making the factors of 750
now once we have completed finding the
prime factors of the number 750 here we
write them in the expanded form
now as we discussed friends in the
factorization mattered
we should make pairs of the similar
factors but here friends we are able to
complete only one pair so in the first
part of the question that is what needs
to be multiplied
whosoever numbers pair is not complete
we have to complete that factor
so I need one two one three and I need
one size that means I need to multiply
the number with 30 so that we can
complete a pair of two as well as a pair
of three as well as a pair of files now
in the second part of the question say
we need to find what needs to be divided
again who forever factors pair is not
complete we will divide by the same
number and eliminated so we are not able
to complete the pair of to end of three
and of five
hence we divide with a 2 a 3 and a 5 and
eliminated so we must divide wet
the same number turkey now let's see the
next question in this question friends
we are given that each student
contributed as many passe as the number
of students in the class and also that
we have to find the number of students
so first of all we let the number of
students
as X some contribution
first student
is also equal to ex passe next steps are
assigned the total money collected so
that total money is equal to X into X
but the units are passe so here I want
to tell you that the units are passe but
in the given question we are given the
collection in terms of rupees hence by
making the equation we will convert the
rupees into passe so the equation is x
squared is equal to 144 in 200
sufferance Y we are multiplying with
this hundred to make the unit's as
passive this is the most important step
so in the next step we take the root
of this number
and the final answer comes out to be 120
which is my required answer now lastly
friends let us have some practice
questions with answer key
Thank You face and happy learning