Numbers & Multiplication
                   Experts say numbers are very vast.From a CAT, XAT, MAT, or from any competative exam point of view numbers is got prime importance.When we talk about numbers the very basic things that we need to know are 4 operations “addition,subtraction,division,multiplication“.Of these the last one is bit time consuming compared to first two.So lets think of steps to reduce time in multiplication .

1. Finding SQUARES with ease
    I have mentioned a few tips in the same topic before,but here are a few more tricks.First of all certain things you need to keep in mind.
           1.While finding a square you must have an idea on how many digits the answer consists of.
   For Eg:- its 2 digit till squares of 9,3 digits till squares of 31,from 32-99 it is 4 digits.

SQUARES in the range 40-50-60
 Take 50 as the BASE number.Think about  number of digits in the answer(Till 99 its 4 digit).

Now an Example will do the explaining job.

• Take 56 as the number whose square is to be found.
• Find the difference with the BASE(50),here it is 6.
• Square of 6 will give last 2 digits of your 4 digit answer.
• For the first 2 digits add the difference 6 to the first 2 digits of the square of the BASE number.
  So first 2 digits are 25+6=31(First 2 digits of the square of BASE number(50*50=2500) =25).
  and answer of 56*56 = 3136

Another Eg:-
59*59=  (25+9)(81)=3481.
52*52=2704.

Now if the number is greater than 40 and less than 50.Same rules apply,but here we will subtract the difference with 50, from the first two digits of the BASE number’s square(2500).
Eg:-
46*46 = (25-4)(16) =2116.
47*47 = (25-3)(09)=2209.

By now i hope you understood what i intended, one very important thing is practice, without which you cannot apply or use these tips, at the right time.

2. SQUARES of numbers greater than 100 till 200.

  This can be done in three steps.I will explain steps first and then elaborate with an example.
STEP:1 Number + Last 2 digits of the number
STEP:2 Find square of last two digits.
STEP:3 Write down STEP2 below result of STEP:1 such that it starts from unit place of the STEP:1’s answer.Add to get the answer.

E.g:-

113*113

STEP1: 113+13=126 +
STEP2: 13*13 =       169
STEP3:                   12769

With these techniques we can considerably reduce time taken.I am telling you all again, workout using some problems.
Eg:-124*124=?
124+24=148 +
24*24 =       576
Answer= 15376

NOTE:1(Important)
153*153=?
153+53=206 +
53*53 =    2809(53 square can be found easily with the other method)
Answer=23409

Here you can see a slight difference,instead of writing the step2 at the unit place, we put it at 10th place or else number of digits in answer will be error.

NOTE:2(Important)
109*109=?
109+09=118 +
9*9  =              81
Answer=11881
See in NOTE:1 & 2 ,knowing the number of digits in the answer comes to play.

Related posts:

1. Numbers & Multiplications PART-2
2. NUMBERS:An important QUAT topic
3. Speed Maths
4. Basic Maths made easy-Speed Enhancing Tips
5. Speed Maths-Fractions