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Mathematics Made Easy – II


by NS Murty  
You must have noticed when the number is above 15 and when you take 10 as base the calculation is somewhat difficult unless you have mastered the squares up to 9. Similarly, when we take 20 or 30 or 70 as base, we will be getting values in 20s, 30s, and 70s. So we must multiply these 20s, 30s, and 70s appropriately by 2, 3 and 7 to convert them to 10s. That is all the adjustment we need to make. Let us see by example. Let us calculate the square of 19.
Let us find the square of 39.
Try 44 square
Thus you can find the square of any number between 1 to100 now. Can't you? Well I know you ask if the number is like 25, 35, 45, 65, etc exactly in the middle of twenties, thirties etc., you do not see advantage of one method over the other. But strangely, you don't need any of these two methods at all. There is nothing simpler than such numbers having 5 in the units place to find the square for. It is the easiest of all things. All you have to do is take the number to the left of 5 and multiply it by its next number and put the product in 100s and always put 25 to the right of it. Just that. Let us see by example. Find the square of 25. Now the number to the left of 5 is 2. The next number to 2 is 3. Then 2x3 is 6 we got 6 hundreds. (I am talking about the place value) Putting 25 to the right of it we get 625.
Now I am sure you can say what is the square of 125. Yes.
How much time did you take to answer this? There is a very interesting corollary, that means, which follows this operation. For any two numbers between the sets of ten like 2129, 3139, 4149 , ... 219220.551559...so on, When the sum of the numbers in the units place is ten, then also the above principle holds. That is multiply the number to the left of units place by its next number and put it in hundreds' place. However the difference now is instead of 25 you will put the product of the two numbers in the units place. Let us study by example: Find the product of 23 and 27. Since 3+7 is ten, the value is 621 See the following table:
Thus it is fun to find the products of numbers. 

12Mar2006  
Views: 8144  




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