How To Find The Square Root of Large Numbers Mentally

[@TheOrganicChemistryTutor]

Radicals - Free Formula Sheet: bit.ly/48lpFLt Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections

[@dasevenaguilar2269]

Love you❤

[@networkhub4306]

This guy is saving my life. I don't need to spend 10 countless minutes figuring out square roots anymore. Give this man a gold medal

[@eaglefangyt]

I know right! Keep up the great work!👍

[@KenFullman]

Since watching this video, how many real life situations have you encountered, where you need to find a square root of a number, and even though you don't know what the square root is, you know it's a perfect square.

[@lonicocopuffs]

I'm definitely going to mention you in my graduation speech, if I'll get elected valedictorian. You're so helpful and your timing is impeccable. I don't know who you are but God sent you to help all students around the globe. Thank you, I'll forever be grateful.

[@vid_studi4371]

Yooo, im doing that when i graduate too!

[@ronalddump4061]

I seriously doubt that you will be valedictorian if you failed to immediately realize that this trick is obviously entirely useless for anything real in maths. That is the reason you were never taught this obvious and simple trick! But explain to me how this trick could EVER be useful for anything! . I am truly interested

[@rafaelpascua7630]

@@ronalddump4061 ehem. Geometry

[@ronalddump4061]

@@rafaelpascua7630 So give me an example of where you could ever us this "trick" to calculate anything in geometry. You cannot. Here, i will help! Suppose you needed to fabricate a spherical water tank that holds exactly 2000 cubic feet of water. You want to find the radius of your tank. Obviously you need to find the CR of some random number in your calcs. NOTICE: This trick cannot help, IN THE SLIGHTEST to accomplish your task.

[@rafaelpascua7630]

@@ronalddump4061 touche. But my point is that it helps finding the final answer incase you don't have a calculator which is actually helpful when I took the military academy exam last week

[@minnicute2497]

I swear you deserve money that I give to my teacher who don't teach me at all. You're always responsible for my success. I hope you live happy life 💞😘

[@ominously2574]

Potatoes Yay good job. You criticised her/him. Good person.

[@potatoesyay7763]

ImT0t4llyL4m3 I’m just giving feedback. I’m sorry if I offended anyone. It’s just that I think more people should fix their English, or at least learn the very basics first. I understand that this might be offensive, but it’s kind of irritating seeing people who can’t even use a full stop properly. (Also, on second thought, minni cute, you english is actually pretty good)

[@ominously2574]

Potatoes Yay I was just telling you that you’re a good sport.

[@potatoesyay7763]

ImT0t4llyL4m3 Ummm.. Are you being sarcastic or are you for real? If for real, thank you.

[@ominously2574]

Potatoes Yay no problem.

[@Meta-Drew]

as long as you only ever run into perfect squares you'll be golden

[@MCConfuz]

Can you explain this more please?

[@Meta-Drew]

@@MCConfuz This trick relies on the assumption that every square you are being given is the square of an integer. Someone might feed you numbers that are the squares of non-integers. Suppose in his original example instead of 1156 it was 1151 if you applied his tricks you would think the answer was either 31 or 39 when in fact its actually 33.92939...

[@MCConfuz]

@@Meta-Drew Do I smell a Rebuttal Video?

[@giovannip8600]

@@Meta-Drew exactly! How deep you calculate the precise root? I guess it's trial and error

[@vali_bg5234]

@@Meta-Drew Well it probably was made for perfect squares, so it is obvious it won't work on anything else. Its like trying to use a fork to eat soup.

[@jojoiii7]

in grade 12 and regret never practicing these properly and was searching a proper and a clear way to do these. thank you so much. helpful as always!

[@RayRay-lo2wn]

I believe this guy’s videos are pure gold...

[@lucasmacdonald753]

Dude you couldn’t have posted this at a better time

[@KatieKennyseattle]

The teacher : " thats wrong " Me: " yeah becuz its a faster way to learn than sitting in class for 8 hours and understand nothing "

[@Robert_H.]

The big problem with your method is that it only works if you are sure that the given root has an integer solution. If you don't know this, you should use the approximation formula Sqrt(n² + a) ≈ n + a/(2n) and (n + 0.5)² = n * (n+1) + 0.25 for better squares between the squares of natural numbers. *RULESET* Given: Sqrt(x) *(1) Remove redundant powers of 10* If x > 1000: 10 * Sqrt(x/100) If x > 100,000: 100 * Sqrt(x/10,000) If x > 10 * 10^(2k): 10^k * Sqrt(x/10^(2k)) New Radikand: y = x/10^(2k) Advantage: 10 < y < 1000 You only need Square numbers of 1 to 31. *(2) Find the closest square number n* Bonus: If the number is relatively centered between two square numbers n1 and n2, you can form the product of these and add 0.25 (n1 * n2 + 0.25) to use the square number (n1 + 0.5)². *(3) Calculate the difference* a = y - n² *(4) Use approximation formula* Sqrt(y) = Sqrt(n² + a) ≈ n + a/(2n) ------------------------------------- Examples: Sqrt(1156) = Sqrt(11.56 * 100) = 10 * Sqrt(11.56) = 10 * Sqrt(12.25 - 0.69) = 10 * Sqrt(3.5² - 0.69) ≈ 10 * (3.5 - 0.69/(2*3.5)) ≈ 10 * 3.4 = 34 Sqrt(2304) = Sqrt(23.04 * 100) = 10 * Sqrt(23.04) = 10 * Sqrt(25 - 1.96) = 10 * Sqrt(5² - 1.96) ≈ 10 * (5 - 1.96/(2*5)) = 10 * 4.8 = 48 Sqrt(4489) = Sqrt(44.89 * 100) = 10 * Sqrt(44.89) = 10 * Sqrt(42.25 + 2.64) = 10 * Sqrt(6.5² + 2.64) ≈ 10 * (6.5 + 2.64/(2*6.5)) ≈ 10 * 6.7 = 67 Sqrt(12996) = Sqrt(129.96 * 100) = 10 * Sqrt(129.96) = 10 * Sqrt(132.25 - 2.29) = 10 * Sqrt(11.5² - 2.29) ≈ 10 * (11.5 - 2.29/(2*11.5)) ≈ 10 * 11.4 = 114 Sqrt(24649) = Sqrt(246.49 * 100) = 10 * Sqrt(246.49) = 10 * Sqrt(240.25 + 6.24) = 10 * Sqrt(15.5² + 6.24) ≈ 10 * (15.5 + 6.24/(2*15.5)) ≈ 10 * 15.7 = 157 And for error estimation for the approximation formula you can use the following term: Error = a²/(8n³) With a < n: Error < n²/(8n³) = 1/(8n) ------------------------------------- Without the 0.5 formula: Sqrt(1156) = Sqrt(11.56 * 100) = 10 * Sqrt(11.56) = 10 * Sqrt(9 + 2.56) = 10 * (3² + 2.56) ≈ 10 * (3 + 2.56/(2*3)) ≈ 10 * 3.4 = 34 Sqrt(4489) = Sqrt(44.89 * 100) = 10 * Sqrt(44.89) = 10 * Sqrt(49 - 4.11) = 10 * Sqrt(7² - 4.11) ≈ 10 * (7 - 4.11/(2*7)) ≈ 10 * 6.7 = 67 Sqrt(12996) = Sqrt(129.96 * 100) = 10 * Sqrt(129.96) = 10 * Sqrt(121 + 8.96) = 10 * Sqrt(11² + 8.96) ≈ 10 * (11 + 8.96/(2*11)) ≈ 10 * 11.4 = 114 Sqrt(24649) = Sqrt(246.49 * 100) = 10 * Sqrt(246.49) = 10 * Sqrt(256 - 9.51) = 10 * Sqrt(16² - 9.51) ≈ 10 * (16 - 9.51/(2*16)) ≈ 10 * 15.7 = 157

[@Mh-gq7rs]

Ok well WTF

[@quianna5096]

..what

[@KJAAICH2]

Ur voice says that ur mind is so clear about this complicated presentation thank you

[@HurricaneEmily]

You can also add the digits of the numbers until you get one digit like if you add the digits of 13 you get 4. If you take the square of 13, it has to add to the same amount as 4x4. 4x4 is 16. 1+6 is 7. So the digits of the square of 13 also have to add to 7. The square of 13 is 169. Add the digits: 1+6+9=16, 1+6=7. So if you can’t tell by looking which is closer, add the digits of the numbers until you get one digit. Take the square and add the digits until you get one number. Look at your two choices and add their digits until you get one number and see which one matches. Let’s say you’re deciding between 43 and 47. The number that is the square of one of these numbers is 2209. 2+2+0+9=13, 1+3=4. What’s the square root of 4? 2. So when you add the digits of the square root of 2209, it has to add to 2: 4+3=7 so it can’t be 43. 4+7=11, 1+1=2. It’s definitely 47. The only time this doesn’t work is when you are choosing between multiples of 3. For example, 42 and 48. The digits of both their squares will add to 9. So you have to guess. These one digit numbers that all numbers add down to are called digital roots. You can add the digits as I did or you can enter a number on a scientific calculator and hit mod 9 to get the digital root. These digits are also the remainders when you divide by 9. Adding them and multiplying them is part of modular arithmetic.

[@fusion9619]

this is my favorite channel. I love this stuff

[@decentassassin2340]

Hey man, I'm speaking as young as 13! Amazing strat, I honestly would ever be amazed to have you as my math teacher but I appreciate the fact that I took this lesson online. I look forward to more of your videos, please keep it up! :D

[@KimmLaulau]

Same age bro!

[@Kobe_Abogutal]

Almost same but 11! I can't believe that I'm learning this so early!!

[@soaringspirits2267]

Xd

[@GG4EVA623]

This only works for perfect squares

[@ronalddump4061]

The reason no math teacher ever teaches it, is because it cannot be used for anything that matters in the real world.

[@cokasoda1439]

this guy can explain better than any of the teachers i know

[@alishbakhan2011]

This guy is helping so much to cover 3 year of classes I had no idea how to solve I only knew perfect squares and now I understand finally after hours of searching the perfect video for me to understand

[@maydad5666]

omg i rlly was struggling thank u rlly so much u rlly deserve the money i pay for the whole school idk why teachers dont teach us this im an 11th grader and i just knew it 😭😭😭😭😭

[@AniketJha-en9nx]

You are the genius brother, saved my time to solve the problems... Thank You Brother..

[@lovernature100]

Glad! SO GLAD The Organic person exist! Not only his voice give a sense of peace and easy mind focusing, he is explain awesomely. Thanks for you! Mr. The Organic

[@gatbos]

These tips and trick you got going on in your videos is what keeps me interested! Haha. Thank you very much.👍

[@Galvezzv]

This is a lifesaver man, I'm participating in a quiz bee and this legit helped me a lot.

[@Unknownname77189]

Love your videos You make math easy and relaxing😉

[@aryanokokok]

Tf u mean relaxing bro I'm having anger issues

[@Firdos250]

Thanks a lot Sir Tomorrow is my exam and I didn't know how to break square root but I will find any root number after watching this video Love from Aligarh, INDIA 🇮🇳

[@paviisthebest]

bro this is too good I will pass most of my exams watching this guy

[@saadmosa258]

Hey mister the organic chemistry tutor, I love you so much

[@ArulAmudhanGuna]

Legend ! 👏🏼👏🏼👏🏼 You deserve some great , cuz these things weren't taught in schools 😥😢.

[@jaimarashid8313]

I was in deep water with these square root of large numbers. Now its seems I've got a lifebuoy to reach the shore. Thank you very much for the video !

[@happycat1435]

after learning this, Me: A father of mathematics has born😂

[@bruh5906]

😂😂

[@currently_in_a_CATRISIS]

😄

[@bernalesjames9110]

susey baka

[@lucasderman4704]

I'm studying for my GMAT and idk why this has never been taught in school. This is the best thing since sliced bread. I owe you my life OP

[@Marcus.9523]

This guy is AMAZING! I was absent last friday because i was ill and missed a lesson. When i got back to school i asked my Teacher what i missed so he asked my classmate to explain, I didnt quite understand because he kept laughing the whole explenation so i just pretended i got it. After class i searched this guy and finally got it. Hes better than my Teacher.❤❤

[@Monstergaming-se7cc]

How many lagends are here 1 day before bord examination 😂

[@MrSmart95]

Hello

[@Queso_Burguesa]

Bro failing the english exam with "bord"

[@Wolgaming-g2r]

Me

[@diegomandragora4327]

C'mon! Perhaps he'd just lost interest in English grammar and got bord so he's given it up. It doesn't mean he is not a lagend.😅

[@GalaticHunter]

​@@Queso_Burguesa fr

[@premamuthukumar5352]

Lovely teaching! Also instead of doing: For example on the square root of 2304: its either 42 or 48 and instead of finding the square root of 40 and 50, you can find the square root of 45 which is in the middle of both numbers. An easy way to work out how to square numbers ending in 5: 5 x 5 is *25,* then keep that. for 45, you have done the 5 and you have 4 left. Add one to that number then times both numbers: 4 times 5 which gives you *20.* Put the numbers together in the order they were in: 4 5 20 25 Your answer is 2025 The original number was 2304 (The number that you had to work out the square root of) which is higher than 2025 so the answer has to be higher too. The answer is 48. Sorry If I didnt explain well, I just think this is a helpful way to do it. It is a bit faster. :)

[@pornimaojha775]

Thankyou! This is really helping me save time instead of performing long calculations, you're being a great help!

[@lemonsquizzyjk]

Man thanks for thinking to upload this ind of tricks to KZbin...ever my tutor never said this to me... amazing thank u you saved my life

[@rishuyadav246]

Lots of love from india, dear sir it helps me alot. ❤❤❤❤❤❤❤❤

[@tfninja_XD]

Thank you so much for this video I was just looking for questions but well I just found a better way in solving square roots. Keep up the good work!

[@deniseg4978]

Thank you so much for the information. I was able to understand and now I feel confident in moving forward to take my exam.!!!!!!

[@geraldcifuni1344]

You are amazing! I have viewed many of your videos on chemistry, physics, and mathematics. All my problems are resolved once I go through your videos. The way you explain how to solve a problem is far superior to any other STEM videos that are seen on KZbin.

[@chepaulinus2495]

You're the best sir, in everything

[@ilikeoranges8784]

There was a mistake in the 15^2 it is actually 225 for people who are confused or thought they remembered wrong but very good method overall!thanks for sharing

[@aaronphillips402]

Will I ever need this? No. But do I know how to do it just in case? Yes. Thanks.

[@jovem3767]

I think you will, if you are at school

[@Zem1e]

@@jovem3767 they would just give you a calculator but would be useful if u can solve it quicker than typing it into a calculator or if u want to impress ur teacher

[@jovem3767]

@@Zem1e yea real

[@ronalddump4061]

In case of what? There is no case in the real math world where this trick could help you with anything

[@tanishq8308]

You are my favorite teacher When you start teach this, I understand in first time. Thank you lot of thank you

[@Xonar_]

omg. im so thankful for this vid i got an entry test and i need this tysm

[@CavalryCharmander]

Huge help, thank you 🙏🏻

[@saptammondal8608]

This is mind-blowing 😮😮😮😮😮... U are the best ❤

[@electricalengineer5429]

One kiss for Square root Trick 😘 Really thankful 👍

[@GOODvibesYT100]

♥️Always I Find Your Videos when I am in trouble with science stuff Love and positive vibes from India🇮🇳♥️

[@catherinecollon9545]

I loved it. Your diction is impeccable. Very helpful. Amusing even.

[@kearaDreen]

I LOVE YOU SO MUCH BRO, I FR LEARNED SOMETHING. YOU’D BE SO GOOD AS MY MATH TEACH I’LL DEFF BE SO GOOD AT MATH IF YOU WERE

[@alnimri]

Now this is really neat!

[@anonymousany9695]

One of the best and easiest way to find square roots.. Thank you so much

[@ronalddump4061]

What is the sqrt of 136.7? This trick did not help much did it?

[@Lastielion]

I love this, so useful. I fell like I was somewhat failed by my mathematics education, realsing in my adult life that other people had been taught long division on paper and Venn diagrams and square roots that I had no idea about. I just thought I was bad at it. But just Googling how to mentally work out square roots, so that I could have rough ideas of perimeters of given areas without having to defer to a calculator I found this. I found it so simple and got it instantly and it reminded me that i am not so bad at numbers. Thank you!

[@varunganesh1164]

Very nice video !!! Love it , just awesome and so useful

[@YTMRCODER]

Tysm man! This helps 🎉

[@BaitMaster22]

I learned so much with this dude, throughout 7th and 8th grade, now I'm in 9th and we are about to discuss factorials, something i learned from this dude when i was in 7th grade. 😅

[@mikiyasayele6833]

you are so smart 👍👍👍 I don't believe there is another person like you 👍

[@sanyasuk.8003]

Thank you. That's help a lot for my tutored students.

[@wasskhan1789]

OMG! Where were you during my schooling ?

[@anaygaur9396]

Probably the best teacher on KZbin. Only this channel can explain us

[@fengyanzhang1666]

You are so amazing! 👍👍👍

[@nykw55]

Method & way of explanation so helpful & brilliant! Thanks Sir!

[@Birdman14k]

omg bro you are the GOAT thank you for this

[@saeatutube2]

I wish i've known this during my school days. Thanks a lot. i'll show this to my kids.

[@davidwellman6422]

This totally works for any digit number, you just need to expand the lines. Each starts one more digit to the right. The first line is digits right next to each other, the next is numbers one apart, the next 2 apart and so on until the last line is the first digit times the last digit. With a little practice, I was squaring a 6 digit number in under a minute.

[@GG4EVA623]

I don’t get it

[@LaraeO]

Can you explain this a little further? I'm not understanding.

[@ronalddump4061]

the vids not about squaring numbers

[@carl-ss1cr]

The people who disliked this [no words] video are the teachers who failed teaching this to their students.

[@ronalddump4061]

Hey dude, they did not teach it, because the trick is totally useless for calculating anything in any real maths situation you will ever encounter in your life. If you didnt quickly notice this fact, you are not doing, (or going to do) very well in maths related subjects.

[@soaringspirits2267]

@@ronalddump4061 all that matters is it helped, whether you learned it differently or not, it doesn't matter.

[@douglasmagowan2709]

One more trick, that really should be here... Taking the example of the square root of 4489, rather than asking if this is closer to 60^2 or 70^2, we consider 65^2 = 60*70 + 25

[@AfsanGul-db2uy]

Many thanks 😊 May God richly bless you ❤😊

[@newfounderchannel4951]

For this video your channel will never rotates back

[@s3ated980]

this is the voice that soothes me, this this is it

[@Shinko-chann]

Thanks guy it helps me alot!! ❤

[@bradinab6637]

thank you for helping my 12 year old, as she is learning this!

[@williamwheeler4344]

An easier way to find the unit digit is to multiply the 10s digit by its next consecutive number. That is 3*4=12. Since 12 is larger than 11 you take the smaller digit 3. If 11 was larger than this product you would take the larger 6.

[@indlamurihemanvitha7718]

Thank you so much sir, I am very glad to have you . I'm from India sir , Thank you so much

[@mattslupek7988]

There’s another way to do it, too. After determining the two possible digits in the ones column, ignore the last two digits, and find the nearest square below the remaining numbers and find the root. That’s the number for the tens column. Multiply that number by the next number up. If the product is smaller than the number left of the ignored digits, pick the larger number for the ones column.

[@EmpyreanLightASMR]

Wish you could write out an example with numbers (like a teacher). Words get me all confused.

[@liliacfury]

@@EmpyreanLightASMR this is where that trick comes from, the guy in the video explains it with examples kzbin.info/www/bejne/pIbcfaGgnKyoo8k

[@jonywashere]

@@EmpyreanLightASMR yeah

[@lilricky5483]

It doesn’t always work I tried

[@lilricky5483]

Try to find the square root of 959

[@prajplayz]

There is also another method mentioned by Presh Talwalkar While finding a root of a number by this method, you may get 2 numbers to decide on. You can take the sqaure of the middle number which would be tge 5th term For example: For root of 24649 You have 2 options: 153 or 157 Now you can take the sqaure of the middle term which would be 155. There is a brilliant trick to find the square of a number ending in 5 Suppose 45 sqaured. Now leave the last digit which would be 5, so you have 4. Now multiply 4 with the number after itself, so: 4*5 which is 20. Now add 25 as the last 2 digits of the number so 45 squared is 2025

[@ChronicTax]

im in pre-algebra and this helps me out a lot

[@santoshghale2796]

Thank you for teaching 😊👋😊👋😊👋😊👋😊👋

[@felixmartinez6686]

Very helpful and correct this is a god send wish you the best

[@dasevenaguilar2269]

You’re so smart! 8:12

[@Wander_draws15]

Its just like we are learning multiplication tables😂😂❤❤❤

[@priyanshibais1869]

Thank you for such valuable info

[@ananyasahoo7021]

Thank you sir ,it is very easy now to calculate any large value of square root ....

[@37rainman]

No it isnt. You can only find the sqrt of a perfect square, which are rare

[@VaibhavEditz380]

Bro, u deserve a platinum medal...

[@jcm5046]

Explaining about squares...etc.. Me: 😐 After trying it to 1156. Me: 🤯

[@demirkdoglu5037]

I am 8th grade I love maths thanks for this video👌👍

[@richardsedcole8098]

A useful trick is that a square of #5 number is # x (# + 1) +25, eg 65 squared is 4225 so you quickly see if you go up or down.

[@zuchrialfarizi]

u mean n*(n + 1) then + 25 in the end? Like 6*(6 + 1) is 42 then add 25 in the end, so we got 4225?

[@bharathishet6412]

Sir🙏My heart felt gratitude to you. I am the average student who thinks maths is difficult that too very weak in Maths. You have made Maths so understandable and I'm loving maths. Salute to you..you made my day sir..🙇‍♀️ My 10th board's are near and I will surely remember you and your tricks in exam hall.

[@gimsbillions]

I love you guys ❤️❤️❤️

[@beinggandhi8966]

Let's use your last example - 24649 Now last digit or we say the digit at unit place is 9 so unit digit of sqrt. Of the given no. Should be either 3 or 7, now the nearest square of a no. is 225 which is equal or smaller than 246, so we take the sqrt of 225, i.e 15 now the desired answer could be either 153 or 157 for that we have to just multiply 15 by 16 i.e 240 (now we will check if 240 is smaller or equal to 246) 240

[@upasnatripathi7733]

Realllllyyyy helpful, I have no words left for you , suck a good teacher

[@TimeHalf]

OH MY GOD THATS SO SMART BRO LIFESAVER ur going in my speech after highschool

[@mikyllaguigayoma8241]

thank youuuuuu i lab you talaga huhuhuhu

[@otherdistractions]

Interesting to see an inspection method for square roots. Does it work with non-perfect sq roots, where we are left with decimals?

[@vaibhavkashyap5277]

You’re a life saver man❤

[@reinzellegamingchannel4532]

His guys is the best i was able to do it know❤😊

[@roanagustin7130]

Exactly what i needed to know !!

[@vali_bg5234]

KZbin Guy better math teacher than math teacher, no big surprise.

[@snikithachordia8868]

Tysm it really helped a lot

[@aianna3814]

1:50 i found something wrong take a look at the 15² it says 215 but the correct one is actually 225

[@JeronMathewThomas-f1k]

Exactly

[@RajnitikDuniya]

Very nice class