Calculate square roots quickly - Vedic Maths tricks in English Video Lecture

Hi, I'm Samir and now we will learn a trick
to find the square root of a perfect
square quickly. Let us begin by taking 21904
as an example.The first step would be to
split the number
keeping the last two digits aside so
we'll get 219 in the first part and 04 in
the second.We observe that 219 lies
between 196 which is 14 square and 225
which is 15 square. The answer would be in
two parts. The first part will get the
number whose square is smaller which in our case is 14. The second part is a bit tricky
to obtain. I would want you to
concentrate on the table given below for
a moment. It shows a mapping of unit
digits of numbers and the unit digits of
their corresponding Squares. Now we can
observe that if a square ends in 1
then then number would have either 1
or 9 as its unit digit similarly
if a square ends in 4 then we have
either 2 or 8, if 9 then 3 or 7 and if 6 then
it would be 4 or 6. In our case the
square ends in 4 so the number can
have either 2 or 8 as its unit
digit. Now, since 219 as closer to 225
will take the larger of the two choices
which in our cases is 8, so we can write
down our final answer as 148. Please note had the number been closer to the
smaller square 196 then we would have
chosen the smaller of the two choices,
2 instead of 8, we will see that in next
example. Now let's take 20164, here again
we will split the number
keeping the last two digits aside so
we'll get 201in the first part and 64 in
the second. We observe that 201 is
also in between
196 which is 14 square and 225 which is
15 square. The first part will get
the number whose square is smaller which in our cases is 14 , for the second part our
choice could be 2 or 8, in this case 201 is closer to 196 so we'll get
2 in the second part.Finally clubbing
these two we will get our final answer as
142. I'll again emphasize that this
trick can be used only when the given
number is known to be a perfect square
if not you will arrive at an incorrect
answer. Let us try to elucidate it a bit
further by taking 76176 as an example
the first step would be to split the
number
keeping the last two digits aside so
we'll get 761 in the first but and 76 in
the second. We observe that 761 lies
between 729 which is 27 square and
784 which is 28 square.The answer would be in 2 parts, the first part would get
the number whose square is smaller which in
our cases 27. Now we move to the second
part ,here the square ends in 6 , so the
number can have either 4 or 6
as its unit digit, since 761 is
closer to 784 will take the larger of
the two choices which in our case is 6, now clubbing these two we can write
down our final answer as 276.
Let us take another example 75076
Here again we will split the number
keeping the last two digits aside so
we'll get 750 in the first part and 76 in
the second .We observ that 750 is
also in between 729 which is
27 square and 784 which is 28
square.So the first part will get the number
whose square is smaller which in our
case is
27.For the second part again our choice
could be 4 or 6, in this case 750
closer to 729 so we will get 4 in
the second part.Finally clubbing these
two will get our final answer as 274.
Thanks for watching,
see you soon!