9th LessonSquaring of numbers

9th Lesson mathematics Tricks and Fun

Hello friends , I am Dr Prema B Sejekan

In this we are going to recapitulate the various methods available to us in the squaring of numbers by Vedic Mathematics.

First we will practice again the squaring of numbers with same digits using the special code . What is the special code?“One more, one less. . Examples given are. - square of ”9999

 9× 9 = 81. We will place 8 on unit place on multiplicand side and 1 on unit place on multiplier side.***8 ***1Now one more than 8 is 9 so three 9 s beside 8 and one !ess than 1 is 0. So three zeroes beside 1.Answer is 99980001

Same way square of 3333 , ,3×3 is 09 So***0 ***9.onemore than0 is 1 and 1 less than 9 is 8 final answer is 11108889

Square of 6666 - 6×6= 36 .we arrange as said earlier ***3 ***6. One more than 3 is 4 and OneLess than6 is 5 so final answer is 444355556

Using the arithmetic progression method from both sides .count the digits first. Totally 10 digits. . 1×1 is 01 In these we have to start from the sides .we will place 0 on multiplicand side and 1 on multiplier side laterally.. increase by 1 till 5 digits on both sides.Thus the answer is 01234 54321

.square of 22222 . 2×2 = 04 So total 10 digits. We will put 0 on multiplicand side laterally and 4 on the multiplier side.Then increase by 4 till 5 digits on either side. So the answer is 0 4,8,12,16 20,16,12,8 4. The Final answer is 0493817284..

Next example- square of five. 4s . 4×4 = 16. 1+6 is ,7 .so increase by 7 on either side. 1 8 15 22 29 34 27. 20 13 6..final answer is 1975269136

Here again squaring of 55555 is shown 5×5 = 25. Now 2+5 = 7 so insert 2 on multiplicand side laterally and 5 on multiplier side laterally. Start adding 7 to 2  we  get 9   then 16, 23. , 30 .  then start from multiplier side . Same way add 7 to 5 and increase by 7 till 5 digit places. Now adding carry overs final answer is 3086358025

Similarly both 7 and 8 also done.

Here square of 998 is given. We can easily do this by Nikhilam sutra. find the complement and write 998-002 so square of 002 gives 004 Then subtract 002 from 998 and the answer is 996 004

Here square of 512 is to be found. we can take base as 500.   ie 1000/2. so 512+012. square of 012 is 144. And 512+ 12 give 524 ..Now 524/2 = 262 ,Final Answer is 262144

The same squaring of 512 can be done differently.

In this base is 100×5 = 500. we take 512+12 ,. Now 12×12 is 144    Now 512+ 12 is 524. this 524 × 5 = 2620 upon adding carry over 1 we get 262144

 Here squaring of numbers with sub corollary of Nikhilam sutra ie “Antyayor Dasake pi” is used . In this type we can add one to tens place one digit and multiply straight,  if ,  in unit’s place digits added together gives 10 and tens place digits are the same. Thus 35× 35 we make it 45× 35 and multiply. Straight gives 1225.. In the second example 25×25 we change it to 35×25 and the answer is 625

In the 3rd example we have 55×55 , we will change it to 65× 55 and the answer is 3025.

Here squaring using Urdhwa Tiryak Sutra is shown..it means vertically and cross wise. In the first example square of 24 so 2×2 is 4   

Then(2×4)×2 is 16. 1 carry over to 4 and 6 in themiddle. now 4×4 is 16 so ,1 carry over and 6 on the side. Final answer is 576

In the second example. Square of three. digits number 386 Is given.

 3×3 = 9; (3×8)2,= 48 4carry over antd 8 beside 9. Next (3×6)2= 36,   8×8 =64 so 36+ 64= 100.we can put one 0 beside 8,' and 0 below 8 and 1 below 9. (8×6)2 we get 96 

 6  beside zero and nine below Zero.

    last 6×6 = 36 6 beside 6 and 3 below 6 so the answer is ,148996.  

Similarly Squaring of 4 digit number is done. 2638and the answer is 6959044.

In the coming class we will study multiplication by Urdhwa Tiryak Sutra Thank you