Finding Square of a Number Video Lecture - Class 8

hello okay this video on squares and
clear roof part 10 is got to you by
example calm no more your car exam now
when we are talking so much about square
you might be thinking that okay for
smaller numbers it is fine but for
larger numbers finding their squares by
actual multiplication could be difficult
so how do we find squares of larger
numbers let's take an example let's say
that I asked you to find out the square
of 64 the 64 square is not something
which you can quickly say or which you
can calculate next week and just give
the answer that's not possible
so what would you normally do if I asked
you to find out the value of 64 squared
so you will perform actual
multiplication that is you would
multiply 64 by itself so 4 into 4 is 16
1 get carry-forward 16 to 24 and 24 + 1
gonna straight to 56 now 6 for the 24th
again 2 is very formal 62 the statistics
+ 2 that is 38 now you add both of these
is become sick 9 chain 4 shows the
resultant force is 96
now you can do the actual multiplication
find out the square of the people but
the chances of missing the chances of
error is this actual multiplication is
growth because either you are doing will
offer calculation using multiplication
will in addition now when your numbers
go even bigger like 64 is one example
now if I ask you to find out the square
of 6 42 square so the multiplication is
going to be more tedious so the chances
of errors is good so to avoid that we
often follows this particular method
when we do not do actual multiplication
but we do something by which the method
of calculation becomes little easier so
64 we can write 64 as 60 + 4 now why did
we write it like this
anyway we have something like 40 50 60
so very will be deal with numbers ending
in zeros solution by default the
computer that is why we want to
represent the given number in terms of a
a multiple of 10 like 50 is a multiple
of 10 so 64 we want to write that 60
plus 40 60 plus 4 square so what does
this mean this means that 60 plus 4 is
getting multiplied to itself that is 60
plus 4 right now how can we write this
now let's see that if you if you would
have had something like this X plus y
into Z how can you write this so if you
have X plus y inside the bracket
multiplied by 8 so this is same as X
into Z plus y into Z this is the same
thing that X multiplied to X plus y
multiplied to Z so this would be the
same thing with a similar way we are
going to do the same thing here where 50
is your X 4 is your wide and 60 plus 4
is your red so therefore we can write it
as 60 into 60 plus 4 plus 4 into 60 plus
4 so now this becomes 60 into 60 so this
is the distributive property if you
remember so this is this is how the
distributive property works a into D
plus C can be written as a into D plus a
into fie 16 to 60 plus 60 into 4 plus 4
into 16 plus 4 into 4 now this
multiplication is alleged PDS because
you have zero to two zeros multiplied
you would get double 0 6 into 6 is 33 6
for the 24 minus B or against it for the
24 1 0 4 into 4 is 16 so when you sum
these up you get 4 0 96 so you get the
same answer the only difference in both
the cases you
take some amount of time but the only
advantage is that in this case using
this technique of using the help of
taking the help of distributive property
the chances of making calculation
mistakes is letter because this time the
calculations that you are performing are
simpler than what you weigh perform
before doing actual multiplication let's
take one more example okay so I think I
have over written that so let's see this
is our next example hundred two squared
102 square so how can we write 102 this
can be written as hundred plus 2 whole
square so this would mean hundred plus
two in two hundred plus two so with the
similar approach we can write hundred in
200 plus one plus two in 200 less to
using the same property as we discussed
here so this becomes hundred plus
hundred hundred in 200 plus hundred into
2 plus 2 into hundred plus 2 into 2 that
is 4 so this becomes ten thousand this
becomes 250 becomes 200 and this is four
so when you find out the sum it is 1 0 4
0 4 so if you here also there was no
need to perform actual multiplication
and you put very easily find out the
square of 102 let's try to find out
squares for numbers ending with 5 that
is those numbers which have 5 at their
unit space or the ones place whatever
you call it
so this is the unit place for one place
this is the tenths place let's say that
we have a number 45 and you have to find
the square of 45 so here also we will
not do actual multiplication instead we
will follow the same technique the K
raised will be one interesting thing now
that you have 45 how can you write 45
you can write it as 4
plus 5 square so this can be written as
40 plus 5 multiplied to itself that is
42 the spice now again with the same
logic this can be written as 40
multiplied to 40 plus 5 plus 5
multiplied to 40 plus 5 so this becomes
40 into 40 plus 40 into 5 plus 5 into 40
plus 5 into 5 so 14 to 40 is 1600 plus
200 plus 200 plus 25 so this comes out
to be 2 0 to 5 so this is the square of
45 now one interesting thing that you
observe is whenever you are trying to
find out square of a number
which ends with find the square also
ends with 5 so you see 5 square many
times so it's quite obvious the square
of any number ending this pipe will
always have a 5 at the end
in fact there is one more similarity
let's look at one more example so that
would help you to understand it better
so let's say that we take 155 155 would
be 1/2 C plus 5 whole square so that
would be 1 2 3 plus 5 multiplied with
150 plus 5 okay I think it was once
we're inside point now let's consider is
155 because virtually started off with
the calculation so this can be very well
written as 150 multiplied to 150 plus 5
plus 5 multiplied to 150 plus 5 so this
becomes 150 into 150 plus 150 into 5
plus 5 into 150 plus 5 into 5 so when it
finds out the product usage 2 2 5 0 0
plus 750 plus 750 plus 25 do you think
you'll also at the end the fourth term
here also the 4025 and this happens for
all numbers which ends with five
so in whichever number you have the
units releases files you normally get to
see the strength way out of these
photons but the last term would be to
incite now a lot of people you know they
give some specific formulas with regards
to these numbers ending in fights but I
really do not believe in you know kind
of memorizing formula and then putting
things into formula so you follow the
same approach as we do for all other
numbers but this is from something
different that you walked up not
difference isn't something unique about
these numbers ending in five so that's
why I brought it to your notice so this
time you are resultant two four zero two
five again a number element five so this
is one very simple way which we
discussed by which you can find out
squares of numbers without doing the
actual multiplication thank you please
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