Perfect and Non Perfect Squares Video Lecture - Class 8

he'll open this video on squares and
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watercourses square the distance
perfect weather integers multiplied to
themself so whenever an integer is
multiplied to itself it gives a perfect
square so you you think of any example
you think of an individual like one so
when one is multiplied to itself you get
one square so this is the perfect way to
multiply to itself you get to square the
values for pull the perfect square three
multiplied still cell three square that
is 9 so 9 is a perfect square
let's take some bigger numbers like 10
multiplied by 10 gives you 10 squared
which is 100 200 is a pocket square if
you have something like curve let's
train 800 multiply it by 800
what is it get it is 800 square which is
6 4 0 0 0 0 there's a big black 40000 so
this is also a perfect square so
whenever you talk about a numbers which
is obtained by multiplying an integer
with itself that number is called a
perfect square
another question is why are we why has
we given this name perfect square is it
that not all numbers have perfect square
because we have so many numbers they
here we see some examples like 1 4 9 16
hundred
yes it's like 40 thousand and so on but
those we think that every number is a
perfect square though that's not the
deal only some numbers are perfect with
in fact that is why we have given this
special name to these numbers let's see
what our non-budget square that means
those numbers which are not perfect
squares and where do they like so now if
you if you very closely observe the
perfect square from the beginning so
then I said beginning I will start
this one so when you see the list you
will see that there are many numbers in
between those perfect squares which are
non perfect with nonfat X squares line
in between perfect square so the
question is how many non-perfect squares
exists between two consecutive perfect
square okay so we will talk about the
number later first let's see it do they
exist between perfect squares let's look
at it so here are all those numbers
which are written in black they are the
perfect way like let's start with
squaring the smallest possible cause of
M in natural number which is 1 xx square
1 you get 1 this is a perfect square the
next possible integer would be 2 when
eclair 2 you get 4 so what about 2 & 3 2
& 3 are missing so 2 & 3 they are non
perfect well because we had squared then
two contributed integers and the result
that we have obtained the results are
not contributed like when we Square 1 we
get 1 but then you square 2 we do not
get 2 we get 4 so what happens 2 & 3
dips bit why you are doing it because
they are not perfect well so there is no
such numbers which when multiplied to
exchange gifts to so mentioned number
and talking about integers similarly
when you square 3 you get 9 so what
happened to the numbers between 4 & 9
like 5 6 7 8 so they remain so these
numbers which are getting missed in
between they are nothing but a
non-perfect square so one more
interesting thing that we also hear is
as the value of the perfect square
increases like earlier it was 1 then 4
then 9 10 16 so as the value of the
perfect squares and increasing do you
notice something that the number of non
perfect squares are also increasing like
initially between 1 & 4 there were two
non-perfect square like between 4 & 9
there are 4 non-perfect square between 9
and 16 there are 1 2 3 4 5 6 non perfect
square and so on so we can eat
and the value of the perfect square and
increasing the number of non perfect
square between them is also increasing
now do you think that a fixed number of
non-perfect squares exists between two
consecutive perfect square so two
consecutive perfect where could be one
and four four and nine nine and fifteen
so how many non-perfect squares exist
between them so from this observation
you would see that between squares of
numbers N and n plus 1 that is 2
consecutive perfect squares there exists
two n non perfect way so if we let's see
that the value of n let n is equal to 1
so if M is equal to 1 that means as per
this statement between 1 and 1 plus 1
which is 2 so between N and n plus 1
that is between 1 & 2
how many non perfect square should exist
to n that is 2 into 1 so there should be
two non perfect square and then we look
at this you see yet there are two non
perfect square 2 & 3 so this formula is
true let's check the same formula for
some other value next table n is equal
to 5 so if n is equal to 5 that means
between the squares of numbers 5 & 6
so between square 2 5 & 6 that means
between 5 square + 6 squared how many
numbers how many non perfect created 2
into n that is 2 into 5 so there should
be n non-perfect squares between v
square + 6 squared let's check it this
is Phi squared this is 6 square so
between PI Square and square we have
these many non perfect square let's and
1 2 3 4 5 6 7 8 9 and 10 so there are 10
lon perfect square so this is a very
simple formula we can be derived after
observing this pattern and this formula
holds true for all the perfect at one
perfect square so whenever you have two
consecutive perfect square
a number of non buckets wedge between
them hood will always be 2n so even put
the corners and isn't you know calculate
how many non perfect squares will exist
between two perfect squares thank you
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