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Square Root II 6-Digit Numbers II Just 10 Seconds II Short Trick II Simplification
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- Опубліковано 19 сер 2018
- The square root of 6-digit numbers are a little difficult to find using the traditional long division method......watch this amazing method to find it in 10 seconds......TOO GOOD FOR COMPETITIVE EXAMS AND FOR STUDENTS OF CLASS VIII AND ABOVE......for more shortcuts, keep watching:
/ @sureshaggarwal
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Sir what about when the question will be find the sqaure root of 6 digit number when it is not a perfect square?
hmm you r right! i will published a video on this tropic shortly... in my youtube channel..
There are couple of tricks by which you can tell a no. Is a perfect square or not one such trick is
1. Digital sum of digits of the number should be either odd or 4 , only then the number will be a perfect square.
For eg. A no. 4725 it's digital sum is 4+7+2+5= 18 which is even so it will not be a perfect square.
@@ksoh1oe276 do you really think 4725 digit sum value is 18....???
@@venkateshpedada7588 I'm literally struggling with formulas of physical chemistry , physics and maths itself and some random guy on UA-cam is teaching me how to do addition ...... 💀💀💀 ..... Well then what is the sum if it's not 18?
@@ksoh1oe276 I didn't mean that but digital sum mean the final answer should be in single-digit brother
dude if you solve them one by one its will be way easier, I started with you but I get lost
I
mohammad alsubaie you are right. I am so confused
Finally, I found the best after spending half my day and it would be the greatest if it includes finding the non-perfect square if it is covers in another video please share the link sir thank you
I know how to do it
Go with long division bro. its also long division somewhat twisted
Hello Sir..amazing method!
I tried your method for various 6 digit numbers and it worked perfectly fine. Had difficulty in finding the square root of 176400,564001 with this method.
I think problem will appear when matching results number at last stage after sum of six digits number
i.e
I Really did it in 10 sec 😂 wow
Sir make square root of 243049
Options are 497and 493
Fantastic trick sir...
Sir, you have taught a simple method to find the square root of Six digit numbers. If you don't mind my suggesting this, we can save much time while adding numbers to find the digital sum.
1. In a string of numbers, we can ignore number 9, since any number added to 9 gives the same digital sum. If we take, for example, 8691987, 8+6=14=5, ignore two 9s and also (8+1)=9 and take last digit 7. That is 7+5=12=3.
If you add 8+6+9+1+9+8+7=48=4+8=12=3.
So, considerable time is saved and also mistakes while adding long numbers is also avoided.
However, this digital sum method doesn't work in a few cases where sum for both possible answers turns out to be the same. For e.g.: 725904, 732736 etc.
How to calculate √259081..??
Sir, what happened in the case of 346921. We get two numbers these are 581 and 589. But both numbers digital sum are equal with the 346921. What will do now.
Will check
It's 589, because the squared number ends in 21. Here's how I know that...
All integers can be written as 50n ± y, where n in an integer and 25 ≥ y ≥ 0. From that, to square an integer, you can do this binomial expansion:
(50n ± y)² =
2500n² ± 2 * 50n + y² =
2500n² ± 100n + y² =
100*(25n² ± n) + y²
Because of that, the y² term is the only one that has an effect on the tens and unit digits of the square number. In your case, you are taking the square root of a number ending in 21. That means y must be 11 (11² = 121). That means that the number you are squaring must be of the form 50n ± 11. Thus, its last two digits must be 11, 39, 61, or 89.
To take advantage of this, you only need to memorize the square numbers up to 25, which isn't too hard. With the exception of numbers divisible by 5, the square of every number from 1 to 25 have a unique 2-digit ending. Those endings, along with 00 and 25, are the *only* possible two-digit endings for a perfect square.
While I'd use that this for square roots, I also use that binomial expansion to mentally square 2-5 digit numbers. This mostly a stupid human trick, but it can be leveraged to do other mental arithmetic like multiplying two numbers that aren't the same.
Multiply 58 by it's next higher number i.e. 59.
58*59=3422
Compare this number with 3469
3469 > 3422
Hence choose the higher number among
581 and 589.
So 589 is our answer.,
This is a wonderful method. I would like to suggest however a way of calculating the final digit. In example 1 for instance the options are 544 or 546. Using 54x55 which is 594x5=2970, it is seen that 2981 is higher, so the answer is the higher option of 546. This can also be verified with the digital roots.
In example 3 the choices are 622 or 628. 62x63=65x60=3900, and 3868 is lower, thus 622. With 786769 it is 883 or 887. We could do 88x89=87x90=7830, as 7867 is higher, the answer is 887. In this case it is clearly the higher as 78 is much nearer to 9^2 than 8^2
Yo chillllll
Thanks. The method which you mentioned comes to the rescue in cases where digital sum of both possible answers turns out to be the same. Like while finding sq. rt. of 725904 (possible answers: 852 & 858; digital sum=9 for both), 732736 (possible answers: 854 & 856; digital sum=1 for both). And there will be plenty 6 digit perfect squares like these.
However, I'd like to mention that the test you used at the end of your comment ("78 nearer to 9^2 than 8^2 so must be 887 and not 883") to verify the answer doesn't always work.
For e.g.: take 243049. Here possible solutions to its sq. rt. come out to be 493 & 497. Again, the digital sum method doesn't yield result as it comes out to be 4 for both. Now, 49x50= 2450 and 2430
@@Abhi-rd4me No, the lower option is correct because 5^2 is over 24
@@tonybarfridge4369 Wait. Correct me if I'm wrong. Proximity test while finding sq. rts. requires that we consider the perfect square lesser than the number (in this case first two digits i.e. 24) and a perfect square greater than it. Then we compare whether our number is closer to the lesser square or the greater square. If it's nearer to the greater square then greater of the two possible solutions is correct and vice-versa. That's why you wrote that last line in your original comment?
Now you're saying, "lower option is correct because 5^2 is over 24". Then I can say for your example 786769 that no, lower option is correct because 9^2 is over 78. But it isn't. What am I missing?!
Dear sir, please kindly solve this question. the square root of 186624 which one is correct between 432 or 438. It looks weird for the results.(Which digits are the same.)
Ans is 432
What if the digital sum of two possible numbers is the same. Example:
Sq root of 243049. Options : 493 and 497.
Thanks for this! I already knew how to get the outer numbers, but just couldn't figure the middle one out.
Great. Do share the links with your WhatsApp groups and contacts
This method may work most of the time but NOT always; for example square root of 725904 yields both the correct answer of 852 and the wrong answer of 858 - the square of the sum of the digits of both come to 9
8+5+2=15; 1+5=6; 6x6=36; 3+6=9 ... 8+5+8=21; 2+1=3; 3x3=9 so you can't distinguish the correct answer :(
It's 852, because the squared number ends in 04. Here's how I know that...
All integers can be written as 50n ± y, where n in an integer and 25 ≥ y ≥ 0. From that, to square an integer, you can do this binomial expansion:
(50n ± y)² =
2500n² ± 2 * 50n + y² =
2500n² ± 100n + y² =
100*(25n² ± n) + y²
Because of that, the y² term is the only one that has an effect on the tens and unit digits of the square number. In your case, you are taking the square root of a number ending in 04. That means y must be 2. That means that the number you are squaring must be of the form 50n ± 2. Thus, its last two digits must be 02, 48, 52, or 98.
Were I to be given 725,904 to take the square root, I would have notices that the number is just bigger than 850² (722,500). The 04 would have clued me into it being 852. If necessary, I would have squared 852 to make sure the original number was a perfect square using the same binomial expansion as above:
(850 + 2)² =
850² + 2 * 850 * 2 + 2² =
722,500 + 3400 + 4 =
725,904
As for recognizing that 722,500 is 850², there is a trick for squaring numbers ending in 5. Namely, drop the 5, multiply the rest by itself plus 1 (i.e., n(n+1)) and append 25 on the end. 85² = 7225; 35² = 1225; 45² = 2025, etc.
Sir, Is this method is only applicable for 6 digits?
Ye. Unless you wanna complicate it
What will be in case of square root of 1258884? Will the sum of digits work here?
112 2==> 6*6=36=9
112 8 ==> 3*3 = 9
1258884 ==> 9
22*22 =4 84
28*28=7 84
12588 84
Both the tricks do not work.
But there is another trick.
1125*1125= 1265625 > 1258884
= 1258884 < 1265625
Hence less number 1122 is the correct answer
Some exceptional number you have given.
=121 484 484
= 121 488 84
= 125 88 84
= 1258884
1122 is the answer.
√243049 = either 493 or 497 .both digital sum is 4 so, how do find correct answer .question NO. 27 in YTC BOOK.
This method does not work for so many numbers for example 121104. If you try to find the square root using his technique you will end up having either 348 or 342. When you use digital sum of the digits both produce 9.
Find square root of 139129.
Just like 337 & 373
34*35 = 1190
1211 > 1190
Hence the number which has greater value i.e. 348 is the our answer.
In the second problem you have made a mistake as 9 x 9 = 18 instead of 81 In this case did not make a diffrence since you were addng the digits
great vid... to all the commenters who say this takes too long are wrong... It becomes second nature once you start using it. After a while you will know what numbers go with what and be able to do the calculation instantly. trust me.
Yea it’s true😊
Sir can you please solve this question 213444...
Sir both are same. 2+1+3+4+4+4 =18(1+8)=9
Ans1 =4 6 2=12= 3 (3×3=9)
2) 4 6 8=18=9(9×9=81=9
So which is correct 🤔 answer...
Sir, when sum of digit of question & both the option are same, then which answer should be picked????
Have you got the solution ..?
I tried to find the square root of a number (732736), using the digital sum method you showed us. The results of square roots I got were ( 854), and (856). The digital sums for all the three numbers (732736) , (856) and (854)come to (1). Then how can I certainly tell people the correct answer in a situation like this?
Multiply 85 by its next higher number i.e. 86
85*86=7310; Compare this number with 36
7327 is greater than 7310.
Hence greater number 856 is the correct answer.
@@nammalwarthiruvengadam2925 thank you sir for taking the time to respond to my question.
@@Tkkj73 you are welcome
Example:337561
By this way，we can guess 581 or 589，But，when we decide which one is correct answer，it fail，because the sum of number to square of 581 or 589 is the same, 25, in this situation, how to judge the correct answer??
337561 → 25 → 7
581 → 14 →5 → 25 → 7
589 → 22 →4 → 16 → 7
Your lectures are really valuable & helpful 🙏
Dear Suresh Aggarwal, if digital sim did not identify which one is the correct answer, then what will we do? For example when we take the square root of 557276 then digital sum not identify...
This is not a perfect squre root number, this method is only for perfect squre root number
Is this method applicable only for problems with a 6-digit number?
Yes see the title
591361 get 761 and 769 and both have single digit 7 in this situation what will I do
769 hoga kyuki 19 ka square = 361
Had a doubt with this same number. Tried the method as explained by sir but the root digit is same which is 7. How to tackle such numbers where the root digit is the same as mentioned above! Please let me know.
Sir if we have 7 numbers or 9 numbers how can we do
One by one please
Really it's a amazing short trick for find out square root.
when I will solve objective question. then I will try last method mean plus method.just find out which options sequel numbers are match with question. and that is answer 😊😊😊
4356 sir what is the answer is 666 if we add this the ans will come 9
but when hre is 7 or 3 as unit digit, then what we can do
If 2,3,7 or 8 is the last digit of any 6 digit number then how can we solve this because there is no number whose square ending with 2,3,7 or 8
Finally understand after searching many UA-cam channels.🙏👍 Great sirji 👍
Kindly share the links with your WhatsApp groups and contacts
It would save a few seconds if you cast out 9's to get the digit sum, Ex 298116, Here you can discard the 9 and 8+1. Leaving 2,1,6 =9.
How did u choose 4,3,2,8 in the division method..i did not understand
6:33 how we can understand which number to choose sir?
Nice, but when the number ends in 2, 3, 7 or 8 ?
then it isn't a perfect square. the method only works for perfect squares
What is this when you doing some of all number then I am not understanding
Realy great
Sir it's a little bit confusing pls can u make a vdo by solving clearly....🙏🙏🙏🙏🙏
Woww it's amazing method sir... Thanks lot to explain dis topic..
Thanks. ...do share the links with your whatsapp groups and contacts
Explain me if u understands
...thank you much i enjoy watching this Math trick ;-) ;-) because i love Math. I wish I had discovered this when i was still in high school..
It's never too late. Do help by sharing the links with your WhatsApp groups and contacts
Root of 0.12 pleas reply sir
0.35
Finally i found the universal technique for 6 digit perfect square root
YOUR GENIUS SIR!!🤩🤩
Thank you sir Your tricks are magnificent😇
Super sir TQ
Do share the links with your friends and contacts
if i have to use the division method so what is the use of the short cut trick?????
your handwriting is nice you taught excellently thank you very much 😊
Sir 126736 is perfect square?
Sir 789 ke square krne pr yeh method use nhi ho rha h
Square of 789 is 62252 and it's digital sum is 8 and the digital sum of 781 is 7 and the digital sum of 789 is 6
Agr sum ko same digit s multiply bhi kia jaye to bhi digit sum same nhi h
So agar digital sum dono ans m s kisi ek que k digital sum k near ho to vahi ans hoga kya..?
Sir how we got to which no. will we take to solve division method ..
Eg - how we know in 2nd question is 6 we will take
Can someone check for number 213444? I am getting 2 options 462 & 468. Both of them are satisfying the ans check.
I liked your handwriting.
Thank you sir
Too good..
Nice trick but what if the number ends with 2 3 8 or something else not perfect
Very good job, sir! Thank you very much!
Very very good trick
Good Day, Sir. It is Ok. Carry on.
Brilliant
How to find the square root of 180625
shubam sawhney 425 ans
very easy sir. I like it.
so..... supper thanks....💜💜💜💜
12x12 is 144... so we should choose only square numbers till 10 ?
Omg! Very very nice sir...
Thanks. Do share the links with your WhatsApp groups and contacts
How identify of square root and not square root
try ^338724 = get two answer 582 and 588 and ALL of them end up 9...so we got 2 answers?
hi sir
i love u teaching very mush
Very nice and easy
Sir very superp and useful
Thanks a lot sir,,,,,
well explanation sir
Thanks. Do share the links with your WhatsApp groups and contacts
Easy tricks sir.thanks.
Thanks. Do share the links with your WhatsApp groups and contacts
Very briliant sir
Thanks. Do share the links with your WhatsApp groups and contacts
Plz check for 412164 in this case root sum is comming same of both that is 9
Super sir. It is very useful for us. Thank you.🙏🙏
Sir, this method not able to find square root of 184041..
it has a decimal place then.. you should be able to end up with a mixed number
Hey Jim - please try again :) the method worked correctly for me = 429
Sir y we don't apply this in option verification
Sir, please solve this 213444. I got same single digit number.
462
Sir, what if the number ends with zero
nice but I want to solve 186624 and 191844.
Good
sir!how can u calculate square root of 0.002?
can u go over...how did u get 104/4 in the top example?
Thank u so much
Superb, mind blowing
"Wow, I appreciate your teaching method which makes solutions so easy and understandable! You have such an amazing teaching style that breaks down complex problems and makes everything click.
Great trick sir...... thank you sir
Thanks. Do share the links with your WhatsApp groups and contacts
Bt sir in 473344 total sum in 1 digit is 7 and answer is 688 it's total is 4 what is this
it is so helpful thank u so much sir
Please solve square root of 99856 from this method
Can you show me the Easy method of doing word problems
No
Thank you this helped me a lot📓🤗
For detailed PDFs of short tricks.....whatsapp +91 9896369963
Sir is there any exception in this rule when we find the square root of 89491y
Sorry no is 894916
16
two possibilities are 944 and 946 . Digital sum of both number is 1.
In that case , multiply 94 by its next higher number and compare with the first 4 numbers in the given number.
94*95 = 8930
8949 > 8930
Hence 946 which has the greater value is our answer.
Thank you so much sir it is a wonderful trick
149590 sir there digital number please sir
sir this method is not suitable for all the number .....just make a try for the number squareroot of 978121!!!!
How do you find the square root of an eight-digit number like 34164025?
Does 64 is closer to 78 or 81 is closer to 78?
Should be definitely less
Of couse 81...such a silly question
Prabin Mandal closer and less