Quick Calculation of Squares

We all are struggling with the problem of efficient and effective calculations. In my recent post I discussed some tips which can make you more efficient in multiplication. Later I found we need to learn the squares from 1-30 for efficient calculations, However I mug up once but later I was unable to recall and there are so many mates like me who feel the same problem. It decipher that  in competitive exams for MBA you can't rely on swotting up. All you need to learn the basic tricks and techniques behind every concept. In this article I will focus on shortcuts to Learn Square from      1-30.

Although learning for one time is not sufficient because practice makes man perfect so you should have to spend 10 Hours in  month to master in calculation and squares play an essential role in calculations.

When you can learn Squares:

If you are trying to learn all the squares in one shot from 1-30 then you are not on correct path. You need to be little strategical and planned. Divide those 30 number in 3 or 4 groups and pick each group one by one. In first shot I focused on learning squares from 11-15 and I assume that you are well aware with squares from 1-9. 

How Can I revise Squares: 

While waiting on bus stop, or while taking shower, You just need to remember  them or murmur them if you feel okay with that. For a while you might think that You are psycho even people around can think but do you really care? My answer for my ownself is no.

How to Calculate Squares:

Download Squares table from Number 1 to 30 .

Squares from 10-20:

While Calculating Square I follow the given methodology:

11= 11(10+1)

12=12(10+2)

13=13(10+3)

14=14(10+4)

15=15(10+5)

16=16(20-4)

17=17(20-3)

18=18(20-2)

19=19(20-1)

20=20(20)

For Squares  from 21-25

Note Down the squares from 21-29

21=441

22=484

23=529

24=576

25=625

26=676

27=729

28=784

29=841

30=900

In the above table can you identify any pattern between squares of 21 & 29, 22 & 28, 23 & 27.

I hope you identified that last two digits of them are same.Thus if you are well aware with squares up to 25 then you can calculate last 5 squares easily and most  of us feels problem here.

I hope you are satisfied with this trick Kindly Share some trick as well. Mistakes are made by humans so kindly correct our mistakes too. We are happy to help you, and I believe knowledge is an only asset which increase with sharing so Kindly share it among your friends.

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Tricks for Quick Multipliation

Everyone who appeared or going to appear in  MBA exam always struggle with problem of  quick Multiplication. When I start solving problems my multiplication speed was quite low.  I thought it would improve with time but it could not  improved then I tried to mug up some most common multiplication but later I realized that this is not solution. In this Article I will share some techniques which makes your multiplication effective as well as efficient.

1) Multiplication By Split Method:

Divide the numbers to the nearest base of 5 or 10 and then do the multiply it.

E.g   I have to multiply 12 and 13. Instead of writing  12x13 I follow the approach given below:

Step 1:12x13= (10+2)(10+3)

Step 2: Do perform the operations separately like (100+30+20+6)=156

2)Multiplication By Base Method:

 This is another method which any aptitude aspirant can use for multiplication of 2 numbers nearby to 100,200,1000,10000 etc. Lets see How I do multiplication using Base Method. 

When Number is nearby 100:

I want to Multiply 107x108

Now Do follow these Steps:

Step1: Split your number in two parts like this (100+7) (100+8) 

Step 2: Since 107 and 108 are nearby 100 so our Base would be 100 

Step 3: See 107 is 7 more than 100 and 108 is 8 more than 100 

Step 4: It would result in 115 

Step 5: Now Multiply 7*8=56

Your Answer for 107 x 108= 11556

It is like (115|56) 107+8=115 and 7x8=56

When Base is not Equal to 100:
When your number is nearby 200, 300 or some other base then you can follow the following techniques:
We are illustrating by multiplying 208 x 211

Step 1: Split your number like above

Step 2: Add 11 in 208 or Add 8 in 211

Step 3:After Adding do multiply it with 2 if base your base  is 200 with 3 if it is 300 or 4 if it is 400
Step4: Do the same above multiply 11 and 8
Get your Answer 211x208=43888
It is like (219*2|88) 2(211+8) and 11x8=88

3)Multiplication By Generalization:

While using Base Method I was always facing problem when I have to multiplication of two digits who has a big difference. After studying and spending countless nights I get a method and learnt this method known as Generalization Method of Multiplication which we usually do in our schools but here I would like to share it in 7 easy steps to of multiplication.

I would like to illustrate by Multiplying it with 243 x 658

Step1: 3 x 8=24

Step 2: 43 x 58= (4x8 +3x5) =47

Step 3: 243 x 658= (2x8 + 4x5 + 3x6)=54

 Step 4:24 x 65= (10+24)=34

Step 5:2 x 6=12

Step 6: After Multiplying arrange them in a sequence like this (12|34|54|47|24)

Step 7: After arranging keep first and last digits same and add the digit diagonal right to it like

1(2+3)(4+5)(4+4)(7+2)4=159894

I hope these techniques would help you in improving calculations. Please share some more techniques and let me know if you any  other trick or technique. 

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