How to square a number
77Squaring Numbers is Easy
My daughter use to struggle when it came to squaring numbers.
Once I explained you're only multiplying any number by itself . If you know how to Square numbers you will save time and look clever. Now my 9 year old thought this would be cool.
Ok so how do you Square numbers dad?
This what I told her.
Image we're going to tile the floor, we would use square ceramic tiles.
All we have to do is count the number of tiles on the vertical side and the horizontal side, then multiply together.
As it a square, the side will be the same, 4 Titles up, X 4 Tiles across (4 X 4 = 16) we would need 16 ceramic tiles.
If 7 Titles Up and 7 Tiles Across (7 X 7 = 49) we need 49 tiles.
Multiplication Table
If you want square numbers around 100
If you want to square numbers around 100 try this trick.
This works with any number under 100 and over 51
- All you have to do work out the difference between 100 and the number you wish to square.
- Subtract the difference from nuber to be squared
- Write this down
Now let's see how this works with 94 squared or (94 X 94)
How to Square Numbers Below 100 and Over 51
Math Puzzles
- If Math Is Boring, Then Math Puzzles Makes Learning Math Fun
If Math Is Boring, Then Math Puzzles Makes Learning Math Fun - Maths is Fun
Piratesmath.com making Maths fun Sharing the Swashbuckling Fun Secrets of Learning Maths
Let's try 97 Square
Alright one more time
Let's try one more
97²
3
94
94(00)
3 x 3 =9
9409
It's pretty easy
Go and practise these, you'll impress your friends
It you get stuck, let me know
Would you like to know how to square any number ending with 5 ?
vote upvote downshareprintflag
- Useful (28)
- Funny (9)
- Awesome (18)
- Beautiful (7)
- Interesting (3)
CommentsLoading...
What about numbers over 100? Do you use the same rule but 1000 as your guide? Then use the resulting difference from 1000 and use the 100 rule? Then you could add the three together!
Squaring any 2-digit numbers, is fairly easy, as follows:
1. Square each digit separately (For example, 84: 8²=64, 4²=16)
2. Append the two results, so that the second occupies 2 digits (in our case, simply 6416, but had the number been 23: 2²=4,3²=9, the result should be 409 and not 49)
3. Now multiply the two digits, and double the result, and append a zero at the end (8*4=32, doubled it's 64, and with the zero, 640).
4. Add the result of (3) to the result of (2): 6416+640=7056=84², and this is the answer.
This trick relies on the identity (a+b)²=a²+2ab+b².
cool
"titles"? err... how about "tiles".
It isn't apparent to me how it works when the difference betwen the number and 100 is over 10. For example, sq of 88=7744 but
100-88=12
88-12=76(00)
12squared=144=76,144 which isn't correct.
So I guess the critical point is that you have to take the last two digits but add the thousand column? 76+1(44)=7744
"So I guess the critical point is that you have to take the last two digits but add the thousand column? 76+1(44)=7744"
I noticed that there was a flaw with the original formula as well. And yes, after having worked it out, it would seem that you -do- have to add the first number to the hundreds column.
Wow... I feel dumb for not knowing this before. :D
I am a Maths teacher, I am impressed by this Mathematics, but please learn how tro spell!
It is cool!
Great hub. Great number works.
LOL I am such a twat - tro = to
Well Thought out
What amazing math trick
Your knowledge on how to square these numbers is amazing.
I thought I was good at maths, back to primary school
wats the ninth square numbaa.?
Not quite sure what you mean by ninth square number
well i guess you'd have to get rather good at this before you can easily find a square of a 2 digit number... until then i'd almost rather just square it by hand..
Solved my little problem this did! Thanks for the excellent hub.What about finding the cube root? I need to work out how big a shipping container is.
great info thank you
great info thank you
thanks so so much this is so much more help full than goggle. this saved my life my mom was buging me about this extracredit about sqareing numbers thanks again so so much
thnx alot! this would help me in our math exploration..wow..
You helped me alot.
Wow awesome but still need troulbe like wat about 2 and 3
i dont get my home work help
what about 1 is that the same as 1(00)
or not help me plz!!!!!! gl?
Well this trick is useful....
untill, you try and use it on numbers around the 50's,60's,70's and 80's because since the difference is greater you will need to multiply larger and larger numbers therefore it would be much easier to stick with numbers in the range 20 at the most from 100.
good trick anyway.
THATS FANTASTIC TRICK
I love doing math because it is so fun ok
nice... i dont know this before..
i got so dumb...
this helped a whole lot with my homework ty for the cool trick ^^ cya
bakwaas.....i didn't get any help!!!!
lolllllllllzzzzzzzzzzzz
This is awesome!!
diidnt help!!!
I like math tricks. But I think that it is better to have real math knowledge for squaring numbers. Let me show an example. I will square the number 62 several ways. look at 60 as 36 because 6 times 6 is 36. Any thing squared in the 60's will have this feature. Take the right most number (2) and add to 36. You now have 38. Next double the 2 and place it next to 38. (384) finally you square the 2, for the final answer 3844.
This is a trick for squaring numbers in the 60's. It is fast the easy to understand. 63^2 is 3966, 64^2 is 7096.
New I will show another trick for squaring 62. This is called "up and down" Look at 62 and go up 2 to 64. Go down to 6 and muliply 64 times 6. It would be helpful if you can think left to right and add 2 to 36 and drop the 4. (36 + 2 of 4)384 is the partial anwser. At the end, you square the last number and add the result. 3844 is the answer. This works on all numbers. This is more like knowledge than just a trick.
i think square numbers are like this 5 squared is 25
nice...but not much....
nice ....but not much.....
if the square of a number is 729. what is the number
Please help!
how do you square a decimal number,for example 5.38,
on a calculator? I thought we just press the "squared" button, but I noticed also that I get a different answer if I enter "shift" first, than the "squared" button on my calculator!! which way is correct????
Cool Trick!
it is easy
IT IS EASY
IT IS SO EASY. HE SIMPLEST THING IVE EVER DONE :)
i think i know how to do it :P
i think it is so very confusing, me and my friends are still trying to figure it out :P
wow. thats like awsome! imma try as soon as i get the hang of it! lolsz xD
wat im stuuuuuuupid loooollll
Hey im Jessie in 6th class and i have a chapter and have to find all the numbers between 50 to 70 , any help it would mean alot ! (:
hi Jessiee_ just try this rule
if you want to square from 50 to 74 then
first of all take the number like 69 in this case
69-50=19
write down the last two digits of square of 19 (361)61
then add this number to 25 and add carry in this case (25+19+3=47) and write it before 61 then square of 69 is 4761
i read your jibberish, and i still don't know how to sqare a number. WTF?
F.U. The reason you couldn't work out all that, "jibberish" is because you are obtuse.Now that you know you are obtuse let me help you.Take out your cell/mobile phone and go to the calculator.Now enter the number you want to square.Now press the "times" button, (hint : it looks like this x ).Now enter the same number as before.Now press the equals button, (hint : it looks like this = ).The big number now on the screen is your answer.So F.U., F.U.2 and to save you looking for the meaning of the word obtuse, let me do it for you.
ob·tuse (b-ts, -tys, b-)
adj. ob·tus·er, ob·tus·est
1.
a. Lacking quickness of perception or intellect.
So Simon says, put your hands on your head.
hi guyz, yesterday i made an equation to find the square of any 2 digit numbers (no 1 proved me wrong or told me tht he already knew it)
i hope this would help, here is the equation: A² (AB×2) B²
:D for example:
34²= (3)² ((3×4)×2) (4)²
= 9 24 16
start from ur right to ur left
now da rule is if u get a 2 digit number after squaring or multiplying (eg: (4)²=16)
then take da first number of the two digits n add it with da number on itz right, n if
it is 1 digit number then kepp it as it is, so now i will add 1 of the 16 with 4 of the 24 n then add 2 of the 24 with 9 n i will get the
answer,
{9+2} {4+1} 6 = 1156 VOWALA!!
sry but da sentence " then take da first number of the two digits n add it with da number on itz right, n if " da word right is wrong itz da number on itz left sry for da mistake
hi guyz, here is another equation made by me but this time itz for 3 digit numbers
(no 1 proved me wron n no 1 told me tht he knew it before) i hope this will help u
n plz comment on them n if u need any question jst ask me, well here is the equation
ABC= A² (AB×2) {B² + ([A×2]×C)} (BC×2) C² (i know tht u say itz 2 long but itz is so simple)
oki how to use:
* always start from left to right
* if u get a 2 digit number after squaring or multiplying then add the frist number
of the 2 digits with the number on itz left
* if u get 3 digit numbers after squaring or multiplying then add the first 2 numbers
of the 2 digits with da number to itz left.
And now for example:
769²=49 (7×6×2) {36 + ([7×2]×9)} (6×9×2) 81
769²=49 84 162 108 81
then do da addtion part be careful
(i will start from da left to da right)
so now i iww add the 8 of the 81 with 8 of the 108 which is 16 so now
1
10 61
wat i did is that i carried up 1 jst like normal addition
now add 10+1 with da 2 of the 162 which is 13
so now 1
16361
now add the 17(16+1) with 4 of the 84 which is 21 so take 1 n carry 2
2
1361
so as 84 is a 2 digit number u will only take da 8 added to 2 which was carried
before n add them both to da 9 of the 49 which is 10+9 which is 19 so now
1
91361
then da last step is add the 1 tht is carried before with da last number which is 4
n now u will get 591361 n u can try it in da calculator it is jst addtion n
simple 1 if u get used to it u will do it fast (i do it in 20 secs)
so gd luk!
hi to make it more simple:
itz simple itz like this
1 2 1 1
769²= 4{9+ 8}{4+ 16}{2+ 10}{8+8}1
= 591361 ! vowala!
hi guyz, to square digit numbers ending with 5 u can do it easily: example
55² take da square of the second number which is 5²=25
n then multiply da first number with da number after it which in this case is 5 (da first number)× 6 (da number after it)= 30
so now 55²= 3025
similarly 15², 25² ........
95²= 9025 (10×9)(5²)
i hope tht i helped
OMG IM IN P6 AND I DONT NO THT :'(:(
Very helpful!!!!!!!!!!!!!!
Karim ur method is really very good.
keep it up !!!!!
Ive got a method to square ANY number of any length...
Multiply it by itself... Damn, that was easy.
omg i am still having soo much trouble with this >(
The above fact is generalized and can be used with any number and any reference number,
Let the number be x,
100{x-(100-x)} + (100-x)^2
=> 100{x-100+x} + (10000+x^2-2*x*100)
=>100(2x-100) + 10000+x^2-200x
=>200x-10000+10000-200x+x^2
=>x^2
squaring a two digit number can also be presented this way:
example:
(64)2 = 4096
Steps:
1. Square the last digit first and place the answer at the right most that would indicate as the last digit in the answer.
If the answer is two digit just drop the last one and carry the right most digit
(4)2 = 16, drop 6 and carry the 1.
2. Multiply the exponent and the numbers + the carry
2x4x6 + 1 = 49; drop the 9 carry the 4
3. Square the left most digit + the carry
(6)2 + 4 = 40, drop 40 as the last process…
4. Combine all the dropped numbers. You have your answer: 4096
Try it…it will work out….
VERY NICE!
Thx so much I really didnt get it
tis is crap
This website is the the most jacked up website ever. $@$%^# THIS WEBSITE! @#$%^
how do i do it with numbers over 100? by the way, nice trick
I LOVE!!!!!!!!!!!!!!!!! THIS THING SO MUCH
i love finding squared numbers so much!!
As explained by Karim squaring numbers 100 to 999, the formula is: ABC = A² (AB×2) {B² + ([A×2]×C)} (BC×2) C², but to make it easier the 'orders of magnitude need to be included.
Using A(10²)B(10)C(1) then the formula ABC² becomes: A².10000 + (AB×2).1000 + {B²+([A×2]×C)}.100 + (BC×2).10 + C².
Try it, makes the final addition a little easier.
PS . = x It just looks neater.
But what about squaring 4 digit numbers (1000 - 9999) I hear you say, well the principle is the same.
(ABCD)² = A².10^6 + 2AB.10^5 + (B²+2AC).10^4 + 2(AD+BC).10^3 + (2BD+C²).10^2 + 2CD.10^1 + D².10^0.
Proof. 1234² = 1².10^6 + (2.1.2).10^5 + (2²+(2.1.3)).10^4 + 2((1.4)+(2.3)).10^3 + ((2.2.4)+(3²)).10^2 + (2.3.4).10 + 4²;
Which becomes: 10^6 + 4.10^5 + 10^5 + 22.10^3 + 25.10^2 + 240 + 16.
1000000
400000
100000
20000
2500
240
+ 16
=1522756
The same principle applies for 5, 6 7 etc digits only the forumla gets very long.
I might post put the 4 digit one early morning.
I'm not a math teacher so know this might not be clear, but the pattern exists to figure squares. Here is a copy of the pattern:
2x2=4
3x3=9 (9-4=5) 5
4x4=16 (16-9=7) 7
5x5=25 (25-16=9) 9
6x6=36 (36-25=11) 11
7x7=49 (49-36=13) 13
8x8=64 (64-49=15) 15
9x9=81 (81-64=17) 17
10x10=100 (100-81=19) 19
11x11=121 (121-100=21) 21
12x12=144 (144-121=23) 23
using the pattern, you'll notice something else. The sum of the 2 squares equals the difference. For example:
2+3=5 (see square on 2's and square on 3's listed above)
3+4=7 (see square on 3's and square on 4's listed above)
4+5=9 (see square on 4's and square on 5's listed above)
5+6=11 (see square on 5's and square on 6's listed above)
and so on and so on. Therefore, the formula would be the square of a number is the previous square value plus the sum of each of the corresponding root numbers or:
square of 21 would be:
Square of 20 which is (400)
plus
20+21 = 41
For a grand total of 441
------
This works backwards as well of course. For example, the square of 89 is:
The square of 90 (which is 8100)
minus
89+90=179
or 8100-179 for a total of 7921
Going to numbers squared further away from the ten squared just means more addition, but still works every time.
For example, the square of 94 is:
90 squared or 8100
plus
(90+91=181)
(91+92=183)
(92+93=185)
(93+94=187)
or 8100+181+183+185+187 = 8836
I'm not sure if this is helpful but it definitely makes doing squares alot easier when you're doing it in your head!
this doesn't make any sense to me what so ever.
Hey,
Just wanted to show where the method above comes from.
you need x2 = x2 - a2 + a2 (adding and sub a2)
= (x-a)(x+a) + a2
that's it.
94^2 = 94^2 - 6^2 + 6^2
= (94+6)(94-6) + 6^2
= 100*88 + 36
= 8836
For finding the square of ANY NUMBER easily, you have to think of binomial expansion. Like what karim had, (A²+2AB+B²) is from the "binomial expansion" of (A+B)^2. just treat A as the tens place and B as the ones place. As karim showed, this can, in a way, be related to squaring three digit numbers.
If you know the lattice method of multiplication and try squaring a number using it, you may notice a patter of writing down the same number. This has to do with binomial expansion. If you dont know lattice, whatever.
If you want to square a number, you better at least know how to square single digits quickly, and how 50²=2500 (if you don't know the second part, just think -- 5²=25, 10²=100
That really helped.
Thanx!
hi
hi
hi
hi
some ppl say it is cool....i think it is cool too but i dunno how to use it * :-(
how do u say that?!? it is super easy!!
hey are you online??
yup i am ALWAYS online to find new math cheats i have a wee problem with maths.... :-D
ohhhh actually i am a straight A student but i got a homework and i didnt know how to do it and i NEVER got less than a mistake in tests
this one is useful 4 a student who is lazy to make a manual calculation, but tnx a lot.... i dont know that.,.,.
thats not called a cheat or trick ,but knowledge
i do not get it
awesome'but still difficult
now i got it .....
it's super easy and cooooooooool
so very easyyyyyyy...................
how do find out the squares of numbers under 51? is there any other trick to find it out? can you please let me know
What is -7 in parenthesis squared?
It's very easy and I thank you very much.
u are the DUDE !!
Well if u just times the number on numbers over ten use the distributive prop
look,i know how to do this but this is butty because this isnt what i was looking for i just need help on some work see here the question is jimmy's restuant has 16 tables that have 4 chair each.how many chairs does he need?but i have to do it in square form can somebody please help if anybody is on here thank you by.
super
wow its so amazing! i can believe it.
i had truble doing it at school but the way you do it is soooo much easyer
The method from 'A' was the best :)
you need x2 = x2 - a2 + a2 (adding and sub a2)
= (x-a)(x+a) + a2
that's it.
It's up to you to decide what x+a should be.
Say we use 50.
x+a = 50
a = 50-x
(x-a)(x+a) + a2
= 50(x - (50-x)) + (50-x)2
= 50(2x - 50) + (50-x)2
= 100(x - 25) + (50-x)2
Basically, for all 2 digit x.
Say 41.
41-25 = 16 50-41 = 9 9x9 = 81
1600 + 81 = 1681.
pasoderholm 4 years ago
To square any number ending with 5 goes like this:
1) Take the first part of the number excluding the 5. Example: 25 -> 2
2) Square the first part and then also add it once. Example cont.: 2 x 2 + 2 = 6
3) Combine the answer with 25 (= 5 x 5, the answer will always end with 25). Example cont.: 6 and 25 = 625. The square of 25 = 625!
Another example: What is the square of 65?
1) 65 -> 6 (removing the 5)
2) 6 x 6 = 36, 36 + 6 = 42
3) 42 combined with 25 -> 4225
The square of 65 = 4225