6th Lesson- squaring of numbers -arithmetic progression

 6th Lesson Mathematics Tricks and Fun squaring of numbers with same digits by arithmetic progression

Hello friends 

 I am Dr Prema B Sejekan.This is the 6th lesson of Mathematics and Fun tutorial.Here we will learn the squaring of 111, 222,444,555.Once we know the technique , however long the number with same digits we can square it.

In this slide squaring of 111 is shown .first we will count the digits in the question.totally 6 digits.so we will mark 6 dots.then we will multiply first lateral digits.1×1= 01.we will place 0 on the multiplicand side lateral end and 1 on the multiplier side lateral end.Thus we start from both sides.Now add 1 to 0 =1, 1+1=2. Then we count from multiplier side 1+1=2, 2+1=3 so the answer is 012 321.the second question 1111×1111 total 8 digits. Answer is 0123 4321. In the third example , one digit is extra on one side so the answer is 01 2 21 ie extra digits place will be occupied by 2(0+2=2 or 1+1=2). Another example  

111 111× 111 here 9 digits 3 digits are extra on one side. Answer is 012 333 321 ie 1+2 =3 or 0+3=3

Same way we will proceed with 2. 22×22 =04 84. In these examples, the digits are increasing by 4 from both sides. Like arithmetic progression. In the second example there is one excess 2 on one side.so middle you put the dot for the extra digit. And proceed working from both sides. 2×2 is 4 we write as 04 since two digiits are involved..write 0 on the multiplicand side lateral corner and 1 on the multiplier side another corner and add 4 to the prev digit from both sides and proceed up. So here 4 dots are there on each side . So on multiplicand side it will be 048 12 and middle dot and on the multiplier side will start from the corner proceed up so it is 48 12 16. How will we fill up middle dot Add digit 0 of multi plicand side with last digit 16 of multiplier side or vice versa. It is 16.so the answer is 0493 7 7284.

If you follow this method you can accurately get the answer however long the squaring is. In this seven 2s are multiplied by seven 2s.  14 digits   Answer is 04812 16 20 24 28 24 20 16 12 8 4.adding the final answer is 0493827 0617284. Practice these you will grasp the method thoroughly.

Here seven 5s are multiplied by seven 2s..totally 14 digits. Now 5×2 is 10. Now write 1 on the multiplicand side lateral corner and. 0 on the multiplier side lateral corner and add 1 each to prev digit. So the answer is 1234567 6543210.

Here squaring of 444 is shown. Total 6 digits. Now 4× 4 =16 digital sum 1+6 is 7.now put 1 on multiplicand side and 6 on multiplier side. Add 7 from both sides proceeding to the centre. Thus here answer is 1+7=8, 8+7 is 15 same way from multiplier side 6+7 is 13: then 13+ 7 =20.thus the answer is 197 136

We will take squaring of four 5s. Ie 5555. Total 8 digits.5×5 is 25 .2+5 is 7. First place 2 on multiplicand side and 5 on multiplier side and proceed to the centre adding 7 to the previous digit . The answer is 2+7 =9: 9+7 is 16 like that. 2 9 16 23 26 19 12 5. The answer is 3085 8025.

In the coming classes squaring of 5s, 7s. 8s and also when these digits are unequal like 555×5555:. 7777× 77777, 88888× 888. Are discussed . Thank you