This is the most common, yet very interesting trick of Vedic Maths.  Using this technique you can find the square of any number ending in 5 very easily.  Given below is the step by step explanation of this squaring technique.

Let us take a 2 digit number ending in 5,

45²

We'll get our answer in 2 parts. The right hand side of the answer will always be 25. The left hand side will be the number other than 5, multiplied by it's successor (next higher integer).

= 4  x  (4+1) | 25

= 4 x 5 | 25

= 2025

( |          stands for concatenation}

Let us try to generalizing the above squaring technique. Say the number is a5 (=10a+5), where 'a' is the digit in ten's place

Square of a5 = a x (a+1) | 25

Similarly we can proceed for 3 digit numbers ending in 5

Square of 195

= 19 x 20 | 25

Left hand side is 19 multiplied by next higher number 20. Right hand side is as usual always 25. Hence the answer

=38025

Few more examples:

95²= 9 x 10 | 25 = 9025

125² = 12 x 13 | 25 = 15625

505² = 50 x 51 | 25 = 255025

Test yourself

Find out the square of 85, 245, 145, 35, 15, and 995?

Using this method of squaring numbers ending in 5, post your answers below. Would love to know your feedback /suggestions too.

Related posts:

1. Trick to Find Square Root
2. How to Find Square of Numbers Ending in 9
3. Shortcut to Find Square of a Number

This method of multiplication from Vedic Maths will make it very easy to multiply two numbers when sum of the last digits is 10 and previous parts are the same. For example multiplications like

23x27 :  Sum of Unit digits i.e. 3+7 = 10; Remaining number i.e. 2 is same in both numbers

46x44:  Sum of Unit digits i.e. 6+4 = 10; Remaining number i.e. 4 is same in both numbers

112x118:  Sum of Unit digits i.e. 2+8 = 10; Remaining number i.e. 11 is same in both numbers

291x299:  Sum of Unit digits i.e. 1+9 = 10; Remaining number i.e. 29 is same in both numbers

135x135:  Sum of Unit digits i.e. 5+5 = 10; Remaining number i.e. 13 is same in both numbers

Solving 46 x 44

You will get the answer in two parts.

First part, to get left hand side of the answer: multiply the left most digit(s), i.e. 4 by its successor 5

Second part, to get right hand side of the answer: multiply the right most digits of both the numbers i.e. 4 and 6.

Example

First part: 4 x (4+1)

Second part: (4 x 6)

Combined effect:  (4 x 5)  | (4 x 6) = 2024

*| is just a separator. Left hand side denotes tens place, right hand side denotes units place

More Examples

37 x 33 = (3 x (3+1)) |  (7 x 3) = (3 x 4) | (7 x 3) = 1221

11 x 19 = (1 x (1+1)) |  (1 x 9) = (1 x 2)  | (1 x 9) = 209

As you can see this method is corollary of  "Squaring number ending in 5"

It can also be extended to three digit numbers like :

E.g. 1: 292 x 208.

Here 92 + 08 = 100, L.H.S portion is same i.e. 2

292 x 208 = (2 x 3) x 10 | 92 x 8  (Note: if 3 digit numbers are multiplied, L.H.S has to be multiplied by 10)

60 | 736 (for 100 raise the L.H.S. product by 0) = 60736.

E.g. 2: 848 X 852

Here 48 + 52 = 100,

L.H.S portion is 8 and its next number is 9.

848 x 852 = 8 x 9 x 10 | 48 x 52 (Note: For 48 x 52, use methods shown above)

720 | ₂496

= 722496.

[L.H.S product is to be multiplied by 10 and 2 to be carried over because the base is 100].

Eg. 3: 693 x 607

693 x 607 = 6 x 7 x 10 | 93 x 7 = 420 / 651 = 420651.

Note: This Vedic Maths method can also be used to multiply any two different numbers, but it requires several more steps and is sometimes no faster than any other method. Thus try to use it where it is most effective

How do you like this Vedic Maths technique, please let us know. You can also share this with your friends.

Related posts:

1. Trick to Find Square Root
2. Vedic Multiplication of two numbers close to Hundred
3. Vedic Multiplication by 9, 99, 999 and so on

The most striking part of this section is that there cannot be any prescribed format to prepare oneself for it. Fortunately, there are some wonderful books which can help you to sail through these competitive examinations. I am listing the most trusted books on current affairs and general awareness below.

Manorama Yearbook 2013 with Free Encylopaedia Britannica CD ROM – This best seller has a long history of success. It is India's best General knowledge update covering almost everything that a student needs in competitive examinations – Purchase Online

Year Book 2013-14 Almanac by Competition Success Review can also be very useful for people preparing for competitive examinations like Bank PO, Bank Clerical and Railways and so on.  – Purchase Online

The Pearson General Knowledge Manual 2013 by Edgar Thorpe, Showick Thorpe– Another awesome compilation of the most useful current affairs and general awareness topics and Q&A for competitive examinations. – Purchase Online

The Pearson Concise General Knowledge Manual 2013 by Edgar Thorpe, Showick Thorpe – This book is the concise   form of the above book. Overall, this is a good book for Government competitive examinations Purchase Online

The links above are affiliate links to Flipkart. I would request you to read the reviews and take opinion of friends and teachers before ordering any book. I shall be glad to add books suggested by you, to the above list. Please feel free to add your suggestions by posting a comment below.

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Remainder Theorem & its application

We have all learnt the Remainder Theorem in class 10 (now i am in 11) that when you divide a polynomial f(x) by x-c the remainder r will be f(c). Now let’s see how we can use this theorem in other situations.

First Example
Let’s consider the following Product: 65 x 32.

We want to find out what is the remainder when it is divided by a number say 7.

To solve such questions we just need find the individual remainders when the numbers are divided by the divisor.

In this case 65 gives remainder 2 (65 -63) and 32 gives remainder 4 (32 - 28) when divide by 7. Multiplying the remainders we get 2*4=8

Since this number is greater than divisor, divide it again by the divisor again, i.e. 8/7 gives remainder 1.

Thus, when 65*32 is divided by 7 it gives remainder of 1. Isn't it amazing! We save time and effort of multiplying large numbers and doing complex divisions.

Second Example
Let’s see another example to find the remainder when 1421 * 1423 * 1425 is divided by 12

By this method 1421 * 1423 * 1425

1st step remainders = 5 * 7* 9 = 35*9
2nd step remainders = 11*9
3rd step remainder = 99/12 = 3

So the monstrous product gives a remainder of 3 when divided by 12.

Third Example
Let’s suppose we want to find the last two digits of the product
22 * 31 * 44 * 27 * 37 * 43

For such problems we just need to find the remainder when it is divided by 100

(22 * 31) * (44 * 27) * (37 * 43)

1st step remainders =  82*88*91
2nd step remainder =  2 * 28

THATS IT!! The last two digits of the lengthy product is found within seconds and as you see it is 56

On behalf of all the QuickerMaths.com users, I  am highly grateful for his contribution.

Related posts:

1. How to find the Remainder upon Division of a Very Large Number?
2. Divisibility Rules for 7 , 11 and 13
3. Find the remainder – Vedic Algebra

Before going further on the method to find the square root, please make a note of the following points –

1) Square of a 2-digit number will have at max 4 digits (99^2 = 9801). That implies if you are given with a 4 digit number, its square root will have 2 digits. Hence, square root of 5 or 6 digit number will be a 3 digit number.

2) This trick works only for perfect squares, it will not work for any arbitrary 4 or 5 or 6 –digit. Check out the method of finding square root of number which is not a perfect square

3) It works only for integers

Now let us start with the trick to find square root in vedic maths way.

Say you have to find the square root of 3481. It must be known that it’s a perfect square.

Now divide this number into two parts. The right hand side should always have 2 digits. Remaining digits will come in left hand side. Do it as shown below.

34            |             81

You know the answer will have 2 digits. Digit at tens place and digit at units place. We will get the digit at tens place using the left hand side of the original number (34) and digit at units place using right hand side of the number (81)

Step 1.

Memorize these tables (very soon you will know why) –

Table 1: Square of 1 to 10

For finding square root of 5 digit numbers you need to know the square of number greater than 10

Table 2: Unit’s digit of Square Roots

Please note that numbers with unit’s digit being 2, 3, 7 and 8 can’t be perfect squares. Hence NA (not applicable) is written in front of such numbers.

Step 2.

For left hand side we need to use table 1. We have to see between which 2 numbers in the 2^nd column do 34 lies. In this case it lies between 25 and 36. So we will take the square root of the smaller number i.e. 25 which is 5.

So 5 is the tens digit of the answer.

Step 3.

For right hand side we need to use table 2. Since our original number (the perfect square) ends in 1 (see 2481), its square root will end in either 1 or 9.

Step 4.

Just observe the left hand side of the number carefully i.e. 34. If it’s closer to larger square in step 2 (36), we’ll choose the bigger number out of 1 and 9.

If it would have been closer to smaller square in step 2 (i.e. 25), we would have taken smaller number i.e. 1 as the unit’s digit

However, in this case 34 is closer to bigger square i.e. 36, hence, the unit digit will be 9 and not 1.

Combining the above results we get the answer as 59.

Thus (3481)^1/2  =  59

Find the square root of 13689, 7921 and 1296. Post your answers below.

I hope you like the trick to find the square root. Leave your comments below.

Related posts:

1. Trick to Find Square of Numbers from 51 to 59
2. Shortcut to Find Square of a Number
3. Finding Cube Root – Vedic Maths Way

It is all about the numbers
Whether numerical or word formulas both of them certainly employ the use of the numbers. Make yourself master of the numbers. Learn the general multiples of all the numbers and make a habit to spend your free time with numbers only. Practice as much as you can and you will be on the right track. You can also figure out something so that you come across these numbers repeatedly. You can paste wallpaper in your room, make some numerical figure as your desktop and subscribe to numerical magazines.

Try to Grip from the Fundamentals and then move forward
Have an approach, which will make youthe basics and fundamentals strong. Once you have a grip over the basics it means half of the work is done. Try to learn what it is all about the “Sutras” and the “Sub sutras” from the starting to the end. What does it all mean? Just solving the examples will not be sufficient but you have to make sure that you have the thorough knowledge of every aspect.

Practice as much as you can
Figures always need practice and you have to make them as your part and parcel. Try to practice every exercise you get your hand on and just solving the problems will not work check the answers also. If you get wrong answers, make sure you look for the right solution and method for a specific problem. There is no end to practice try as many problems as you can since Vedic math is meant to shorten your normal problem solving time pay special attention to any shortcuts you come across and learn them by heart.

Try to Get some Good References
It is always recommended to follow some trusted books. It is always true that right teaching and guidance can do wonders and you have to search both of these for you to get into the right direction. You can follow some good reference books and take some guidance in the form of internet, magazines, friends and family members.

Some Mind and Brain Exercise can do wonders
Since Vedic math is all about the mind, you can learn a few exercises so that your brain is fresh while you start studying the Vedic math.In addition, you can learn how to refresh your mind after several intervals.

Keeping in mind the above tips will certainly give you an edge over the others in learning Vedic math and you can solve lengthy and complicated calculations beating the calculator after learning this math.

Author Bio
Claudia is a talented writer who has performed her duties well. She had taken up various assignments about IT Jobs training. She loves to share her knowledge and expertise with other people through her articles, follow me @ITdominus1.

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Select any three-digit number with all digits different from one another. Write all possible two-digit numbers that can be formed from the three-digits selected earlier. Then divide their sum by the sum of the digits in the original three-digit number.

You’ll always get the same answer, 22. Isn’t this wonderful!

For example, take the three-digit number 786. The 2 digit-numbers which can be made using the digits 7, 8 and 6 are 78, 87, 76, 67, 86, 68. Hence sum = 78 + 87 + 76 + 67 + 86 + 68 = 462. Sum of digits of 786 = 7+8+6 = 21. Then 462/21 = 22

This will be true for any three-digit number with all digits different.

If we go deeper and try to analyze this unusual result, we’ll be able to appreciate the usefulness of algebra.

In this case the general representation of any three digit number with all digits different will be 100x+10y+z.  Now to find the sum of all the two-digit numbers taken from the three digits

= (10x+y)+ (10y+x)+(10x+z)+(10z+x)+(10y+z)+(10z+y)

= 20(x+y+z) + 2(x+y+z)

=22(x+y+z)

This when divide by the sum of the digits, (x+y+z), is 22.

This shows the importance of algebra in explaining such simple yet interesting mathematical phenomenon.

If you know about such interesting properties of any number post it here as a comment below or email it to me at vineetpatawari [at] gmail [dot] com

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The Six Thinking Hats method may well be the most important change in human thinking for the past twenty three hundred years

I’ve just quoted the first line of the preface of the book “Six Thinking Hats” by Edward de Bono. The Six Hats method is an amazingly simple technique based on the brain’s distinct ways of thinking.

Brainstorming sessions or meetings are unavoidable part of our life. However, mostly these produce no results and waste lot of time. This technique, named as Six Thinking Hats by its founder Edward de Bon, is thinking from different perspectives about a decision to be made. This forces you to think outside your habitual way of thinking and helps you to get an overall view of a situation.

Lot of people mostly think from a critical or negative point of view. On the other hand, many successful individuals think from a very positive viewpoint. However, it becomes difficult for them to analyze the issue from various angles like intuition, emotion, creativity, etc. This may result in unnecessary attachment to a plan and thus underestimating the opposition, if you’re too positive about it. Similarly, cynics may be excessively defensive and emotional individuals may fail to look at the problem rationally with peace of mind.

How to use the method?  Or  What each Hat denotes?

Whita Hat – Everyone in the meeting just thinks and analyses data, information, past trends, facts and figures.

Red Hat – You look at the problem using gut feeling, emotions and intuition without caring about logical reasoning

Black Hat – looks at the negative points, possible flaws, risks and thus helps in creating a contingency plan and helps in eliminating the week points of a plan.

Yellow Hat – it talks about good things and thus presents an optimistic point of view. It helps in gloomy situation when no one is ready to think about positive outcomes.

Green Hat – it signifies creativity, hence coming up with out of box solutions to a problem.

Blue Hat – person wearing blue hat directs the group on usage of various hats. Normally, the chairman of a meeting assumes this role.

The book Six Thinking Hats is worth reading to understand proper way of using this powerful technique. I’ve given the affiliate link of flipkart, in case you would like to order it online.

Edward de Bono has written many books but according to me some of his amazingly superb and game changing books are -

Lateral Thinking

Teach Yourself to Think

Teach Your Child How To Think

A Beautiful Mind

I Am Write You Are Wrong

Hope you enjoy reading these books. Let us all know your opinion if you’ve already read these books.

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We have two one litre bottles. One contains quart of milk and the other quart of water.  (1 quart = 0.9463 liters) We take a tablespoonful of milk and pour it into the water. Then we take a tablespoon of this new mixture (water and milk) and pour it into the bottle of milk. Is there more milk in the water bottle, or more water in the milk bottle?

To solve the problem, we can figure this out in any of the usual ways— often referred to as “mixture and alligation problems”—or we can use some clever logical reasoning to find out the problem’s solution.

Post your solutions below as comments.

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Amazing property of 1089

Select a three digit number (where the units and hundreds digits are not the same) and follow these instructions:

Step 1: Choose any three-digit number (where the units and hundreds digits are not the same).

Let us randomly select the number 469

Step 2: Reverse the digits of the number you have selected

So reverse of 469 is 964

Step 3: Subtract the smaller number from the bigger one

964 – 469 = 495

Step 4: Once again reverse the digits of this difference

Reverse of 495 is 594

Step 5: Add the last two numbers

594+495 = 1089

This result will be the same for any 3-digit number chosen in step 1. Isn’t it astonishing that regardless of which number you select at the beginning, you will get 1089 as the result.

Another property of 1089

Let’s look at the first nine multiples of 1,089:

1089 x 1 = 1089

1089 x 2 = 2178

1089 x 3 = 3267

1089 x 4 = 4356

1089 x 5 = 5445

1089 x 6 = 6534

1089 x 7 = 7623

1089 x 8 = 8712

1089 x 9 = 9801

I am sure you notice a pattern in the products. Look at the first and ninth products. They are the reverses of one another. The second and the eighth are also reverses of one another. And so the pattern continues, until the fifth product is the reverse of itself, known as a palindromic number

Another unique property of 1089

33^2 = 1089 = 65^2 – 56^2

The above representation is also unique among two digit numbers.

We must agree that there is a particular beauty in the number 1089. What is your opinion?

Related posts:

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2. Vedic Multiplication Trick
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