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Finding the square of a number - Vedic Maths tricks Video Lecture | Improve Your Calculations: Vedic Maths (English) - Class 6
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FAQs on Finding the square of a number - Vedic Maths tricks Video Lecture - Improve Your Calculations: Vedic Maths (English) - Class 6
| 1. What is Vedic Maths? |  |
Vedic Maths is a system of mathematics that originated in ancient India. It is based on the ancient Hindu scriptures known as the Vedas and offers various mental calculations and shortcut techniques to solve mathematical problems quickly and efficiently.
| 2. How can Vedic Maths help in finding the square of a number? | |
Vedic Maths provides several tricks and techniques to find the square of a number mentally. One such technique is the "Vertically and Crosswise" method, where the number is split into its tens and units digits, and the square is calculated using cross multiplication and addition.
| 3. Can you explain the "Vertically and Crosswise" method for finding the square of a number? | |
Sure! In the "Vertically and Crosswise" method, let's take an example of finding the square of a two-digit number, say 45. First, we calculate the square of the tens digit (4^2 = 16). Then, we cross multiply the digits (4 * 5 * 2 = 40) and add it to the previous result (16 + 40 = 56). Finally, we append the square of the units digit (5^2 = 25) to the end. Thus, the square of 45 is 2025.
| 4. Are there any other Vedic Maths tricks for finding squares? | |
Yes, apart from the "Vertically and Crosswise" method, Vedic Maths offers other techniques as well. One of them is the "Nikhilam" method, which is based on the concept of complements. This method is particularly useful for finding the squares of numbers close to a base number.
| 5. How can I learn and practice Vedic Maths techniques for finding squares? | |
There are various books, online resources, and even courses available to learn Vedic Maths techniques. It is recommended to start with basic concepts and practice regularly to become proficient in using these mental calculation methods. Additionally, solving practice problems and applying the techniques to real-life scenarios can further enhance your skills in finding squares using Vedic Maths.
Text Transcript from Video
Hi I'm samir, and now we will learn some
techniques to find the squares of numbers.
Let us begin by trying to calculate the
squares of numbers which are close to 50. Let
us take 58 as an example. The first step
would be to determine the difference
from 50. So 58-50 is +8 .Now we
can proceed to write down our answer which would
be in 2 parts. The first part would be 25 +
the difference and the second part would
be the difference square, so in our case
the first part would be 25+8, 33
and the second part would be 8
square, which is 64. So we can club
these two and get out final answer as
3364. Let us take 44 as an
example now.Let us begin by trying to find the difference, 44-50, would be -6. Now we
can proceed to write down our answer which would be in 2 parts, the first part would be
25+ -6, giving us 19 and the second
but would be the square of difference which
in our case is -6 square, 36. Clubbing these 2 we will get our final answer as
1936. Let's take 53 of an example, here
the difference from 50 would be
+3. Now we can proceed to write down
our answer which would be in 2 parts.
The first part would be 25 plus three which
is 28 and the second part would be
the square of the difference which is 3 square in our case which will give us 9. Now we have
to remember that the second part will always have 2 digits, so we will have to add an extra
0 in front of 9 making it
09. We can now club these 2 parts and get our final answer as 2809. Let us now try to
find this square of 37. The difference
from 50 would be -13 . We
can now proceed to write down our answer which would be in 2 parts. The first
part would be 25 + (-13 ) which will
give us 12 and the second part would
be the square of the difference,which in our case is
-13 square giving us 169.Since our second part can have only 2 digits the
extra 1 will be carried over to the
first part making it 12+ 1, 13
and will be left with 69 in this second
part giving us our final answer as 1369.
Let us now try to find the squares
of numbers which are close to a base.
Let us begin by taking 1003 as an example.Here our base would be 1000 and the
difference would
be +3. Now we can proceed to write down
our answer which would be in 2 parts. The
first part would be the number added to
the difference ,which would be 1003 plus
3 giving us 1006 and the
second part would be the square of
the difference which in our case is 3 square giving us 9. Now, here we have to note that
our base had three 0's so the second
part will have 3 digits. so we will have
to add extra two 0's in front of 9 giving
us 1006009 as our final answer. Let us
now try to find the square of 127. Here our base would be 100 and the difference
would be + 27. We can now proceed to write down our answer which would be in 2 parts.
The first part would be the number added to the difference which in our case is
127 + 27, giving us 154 and the second
part would be the square of the difference
which in our case is 27 square
giving us 729.Now , since the second part
can have as many digits as the number of 0's in our base, the extra 7 will be
carried over to the first part giving us 154
plus 7 as 161 and we will be
left with 29 in the second part. Clubbing these 2 we will get our final answer as
16129. Let's now take 86 as
an example. Here again our base would be
100 and difference would be -14.
Now we can proceed to write down our
answer which would be in 2 parts. The first part would be the number added to the
difference which in our case is 86 + (-14) which will give us 72
and the second part would be the square of the difference which in our case is
-14 square and giving us 196. Again
the second part cannot have more digit
than the number of 0's in our base which in our case is 2. So the extra 1 will be carried to
the first part making it 72 +1 , 73, and we will be left with 96 in the second part giving us our final
answer as 7396. Let us now try to find the
squares of numbers which are close to
the multiple of the base. Let us begin by taking 207 as an example
Here our working base would be 2x 100 with multiplier as 2 and the difference .
would be +7. We can now proceed to
write down our answer which would be in 2
parts. The first part would be the number
added to the difference which gives us
207 + 7, 214. Since
our multiplier is 2 we will have to multiply 214 with to get
428 and the second part would be the
square of the difference which in our
case is 7 square and giving us 49. So we can club these two and get our
final answer as 42849. Let us now
try to find the square of 397. Here
our working base would be 4x 100 with 4 as our multiplier and the difference would be -3.
Now we can proceed to write down our
answer which would be in two parts the first
part would be the number added to the difference which in our case is
397+ (- 3 ) giving us 394. Now, since
our multiplier is 4 we will have to
multiply 394 with 4, which is equivalent
to saying 4x (400-6) giving us 1600
minus 24
1576 as the answer in the first part and
the second part would be the square of
3 giving us 9. Now since we have
two zeros in our working base , we will have
to have to 2 digits in the second part. So we will have to add an extra 0 to the 9 making
it 09. Now we can club these two
parts and get our final answer as
157609. Let us now trying to find the square of 421, here
our working base would be 4 x 100 with 4 as our multiplier and
the difference would be + 21. The
first part of the answer would be
number added to the difference which would be 421+ 21 giving us 442.
Since we had our multiplier as 4, we will
need to multiply 442 with 4
giving us 1768 as our first part.The
second part would be the square of the
difference which would be 21 square giving us 441. Since the number of 0's in our working
base is two, we will have only two digits in
the second part ,therefore the extra 4
will be carried over to the first part
making it
1768 +4, 1772 and we will be left with
41 in the second part.Now clubbing these
two, we will get our final answer as 177241.This is it for now, lots of new stuff coming your way
stay tuned.
techniques to find the squares of numbers.
Let us begin by trying to calculate the
squares of numbers which are close to 50. Let
us take 58 as an example. The first step
would be to determine the difference
from 50. So 58-50 is +8 .Now we
can proceed to write down our answer which would
be in 2 parts. The first part would be 25 +
the difference and the second part would
be the difference square, so in our case
the first part would be 25+8, 33
and the second part would be 8
square, which is 64. So we can club
these two and get out final answer as
3364. Let us take 44 as an
example now.Let us begin by trying to find the difference, 44-50, would be -6. Now we
can proceed to write down our answer which would be in 2 parts, the first part would be
25+ -6, giving us 19 and the second
but would be the square of difference which
in our case is -6 square, 36. Clubbing these 2 we will get our final answer as
1936. Let's take 53 of an example, here
the difference from 50 would be
+3. Now we can proceed to write down
our answer which would be in 2 parts.
The first part would be 25 plus three which
is 28 and the second part would be
the square of the difference which is 3 square in our case which will give us 9. Now we have
to remember that the second part will always have 2 digits, so we will have to add an extra
0 in front of 9 making it
09. We can now club these 2 parts and get our final answer as 2809. Let us now try to
find this square of 37. The difference
from 50 would be -13 . We
can now proceed to write down our answer which would be in 2 parts. The first
part would be 25 + (-13 ) which will
give us 12 and the second part would
be the square of the difference,which in our case is
-13 square giving us 169.Since our second part can have only 2 digits the
extra 1 will be carried over to the
first part making it 12+ 1, 13
and will be left with 69 in this second
part giving us our final answer as 1369.
Let us now try to find the squares
of numbers which are close to a base.
Let us begin by taking 1003 as an example.Here our base would be 1000 and the
difference would
be +3. Now we can proceed to write down
our answer which would be in 2 parts. The
first part would be the number added to
the difference ,which would be 1003 plus
3 giving us 1006 and the
second part would be the square of
the difference which in our case is 3 square giving us 9. Now, here we have to note that
our base had three 0's so the second
part will have 3 digits. so we will have
to add extra two 0's in front of 9 giving
us 1006009 as our final answer. Let us
now try to find the square of 127. Here our base would be 100 and the difference
would be + 27. We can now proceed to write down our answer which would be in 2 parts.
The first part would be the number added to the difference which in our case is
127 + 27, giving us 154 and the second
part would be the square of the difference
which in our case is 27 square
giving us 729.Now , since the second part
can have as many digits as the number of 0's in our base, the extra 7 will be
carried over to the first part giving us 154
plus 7 as 161 and we will be
left with 29 in the second part. Clubbing these 2 we will get our final answer as
16129. Let's now take 86 as
an example. Here again our base would be
100 and difference would be -14.
Now we can proceed to write down our
answer which would be in 2 parts. The first part would be the number added to the
difference which in our case is 86 + (-14) which will give us 72
and the second part would be the square of the difference which in our case is
-14 square and giving us 196. Again
the second part cannot have more digit
than the number of 0's in our base which in our case is 2. So the extra 1 will be carried to
the first part making it 72 +1 , 73, and we will be left with 96 in the second part giving us our final
answer as 7396. Let us now try to find the
squares of numbers which are close to
the multiple of the base. Let us begin by taking 207 as an example
Here our working base would be 2x 100 with multiplier as 2 and the difference .
would be +7. We can now proceed to
write down our answer which would be in 2
parts. The first part would be the number
added to the difference which gives us
207 + 7, 214. Since
our multiplier is 2 we will have to multiply 214 with to get
428 and the second part would be the
square of the difference which in our
case is 7 square and giving us 49. So we can club these two and get our
final answer as 42849. Let us now
try to find the square of 397. Here
our working base would be 4x 100 with 4 as our multiplier and the difference would be -3.
Now we can proceed to write down our
answer which would be in two parts the first
part would be the number added to the difference which in our case is
397+ (- 3 ) giving us 394. Now, since
our multiplier is 4 we will have to
multiply 394 with 4, which is equivalent
to saying 4x (400-6) giving us 1600
minus 24
1576 as the answer in the first part and
the second part would be the square of
3 giving us 9. Now since we have
two zeros in our working base , we will have
to have to 2 digits in the second part. So we will have to add an extra 0 to the 9 making
it 09. Now we can club these two
parts and get our final answer as
157609. Let us now trying to find the square of 421, here
our working base would be 4 x 100 with 4 as our multiplier and
the difference would be + 21. The
first part of the answer would be
number added to the difference which would be 421+ 21 giving us 442.
Since we had our multiplier as 4, we will
need to multiply 442 with 4
giving us 1768 as our first part.The
second part would be the square of the
difference which would be 21 square giving us 441. Since the number of 0's in our working
base is two, we will have only two digits in
the second part ,therefore the extra 4
will be carried over to the first part
making it
1768 +4, 1772 and we will be left with
41 in the second part.Now clubbing these
two, we will get our final answer as 177241.This is it for now, lots of new stuff coming your way
stay tuned.
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Nov 19, 2024 Last updated |
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