Perfect Squares

Beat the clock to name the squares of these numbers.
Answer must correspond to highlighted box
Quiz by vlm64
Rate:
Last updated: November 14, 2018
You have not attempted this quiz yet.
First submittedNovember 11, 2012
Times taken72,365
Average score63.3%
Rating4.41
2:00
Enter number here:
0
 / 30 guessed
The quiz is paused. You have remaining.
Scoring
You scored / = %
This beats or equals % of test takers also scored 100%
The average score is
Your high score is
Your fastest time is
Keep scrolling down for answers and more stats ...
Integer
Square
1
1
2
4
3
9
4
16
5
25
6
36
7
49
8
64
9
81
10
100
11
121
12
144
13
169
14
196
15
225
16
256
17
289
18
324
19
361
20
400
21
441
22
484
23
529
24
576
25
625
26
676
27
729
28
784
29
841
30
900
+9
Level 59
Dec 24, 2012
Got 'em all with 25 seconds left. Great quiz!
+3
Level 63
Dec 24, 2012
21/30 :)
+1
Level 57
Dec 24, 2012
i got 24/30 on the first try. 28/30 on my second and 30/30 on my third =) i think that's good...
+8
Level 23
Dec 26, 2012
We all thankfully know what 1 squared would equal to.
+18
Level 83
Jun 23, 2014
Yet curiously we don't all know 2 squared.
+1
Level 71
Jan 13, 2021
lol yeah
+5
Level 62
Jan 14, 2021
hmm what's one times one? one, duh. what's two times two? uhh, maybe 5? or 3? or 160?
+1
Level 35
Dec 28, 2012
26
+1
Level 20
Jan 28, 2013
only got 1-13, without using a calculator
+17
Level 83
Dec 18, 2018
You can calculate them step by step in your head by adding to the previous sqaure the sum of the number you are squaring and the previous number you squared.

1²=1

2²= 1²+ (2+1)= 4

3²= 2²+ (3+2)= 9

4²= 3²+ (4+3)= 16

and so on.

+3
Level 66
Sep 25, 2019
That seems to take much more time, maybe usefull in higher numbers, like 97
+2
Level 60
Sep 28, 2020
Look at the difference between one square and the next. for the next square, add two to the difference and add that to the previous square. 4 - 1 = 3. 3 + 2 = 5. 5 + 4 = 9 = 3 times 3.
+1
Level 64
Mar 26, 2023
1^2 = 0^2 + 1

2^2 = 1^2 + 3

3^2 = 2^2 + 5

4^2 = 3^2 + 7

n^2 = (n-1)^2 + (2n-1)

+1
Level 64
Mar 26, 2023
n^2 = (n-1)^2 + (2n-1)
+1
Level 64
Mar 26, 2023
n^2 = (n-1)^2 + (2n-1)
+1
Level 64
Mar 26, 2023
n^2 = (n -1)^2 + (2n -1)
+1
Level 37
Sep 25, 2013
Got 30 out of 30, with 0:14 left.
+3
Level 48
Jan 2, 2014
1:07 left. This quiz was great, perhaps extending to 50 may deem more conducive, for I have memorized all perfect squares to 33.
+2
Level 62
Dec 1, 2014
Got em all with about 15 seconds left and that felt great!!

28^2 and 29^2 were my hardest two ... b/c I didn't have any clue what those two were off the top of my head... so I just went about doing 28^2 = (30-2)^2 = 900 - 2(-2 x 30) + 4 {which is just a quick way of multiplying those two binomials together} ... and this gave ---> 900 - 120 + 4 = 784 !!!!

Similarly, 29^2 = (30 - 1)^2 = 900 - 2(30 x 1) + 1 = 900 - 60 + 1 = 841 !!!

+1
Level 58
Jan 15, 2015
1:08 left
+8
Level 63
Jan 22, 2015
Pretty easy so long as you know the trick to just adding the last difference plus 2 every time.
+1
Level 66
Jan 13, 2021
Yep, I had to use that method for the upper teens, lower twenties, and upper twenties. Only have 1-13, 20, 25, and 30 memorized. Definitely would not have had time had I tried to multiply the ones I didn't have memorized.
+1
Level 38
Feb 6, 2015
Did it all in my head... 38s remaining
+1
Level 38
May 21, 2015
1 minute left no calculator XD
+1
Level 77
Jul 5, 2015
Got the first 28. Could have easily gotten the last one (30 squared = 900) but I didn't think to until time was almost up.
+2
Level 56
Jul 5, 2015
Gotta love the image of squares that is used for this quiz.
+1
Level 22
Dec 4, 2022
Yes
+1
Level 58
Sep 8, 2015
Yay, 28 secs left, maths class really payed off!
+1
Level 35
Nov 27, 2015
30/30 with 50secs left.... Well chuffed
+1
Level 10
Apr 10, 2016
I got all the way up to 28^2=784 :)
+1
Level 95
Dec 11, 2016
1:05 left on the clock. And I was slow due to writting on laptop.
+1
Level 78
Jul 11, 2017
Did it past 12 with a calculator. Got 4 points. Now ashamed of myself
+3
Level 71
Oct 7, 2017
So you should be ......... 2 smacks on the left pandy.
+1
Level 71
Jan 28, 2018
33 sec left
+2
Level 48
Aug 13, 2018
1:43 left on the clock. Stop bragging now.
+2
Level 67
Oct 3, 2018
There is a good trick with perfect squares in ascending order.

You just take the difference of the last two squares and add two to it. Then add this to the last square. For example:

20^2 = 400. This is 39 greater than 19^2 (361). Add two to 39 to get 41. Then add this to 400 to get 21^2.

Saves getting the calculator out as it becomes simple addition.

+1
Level 75
Oct 26, 2018
This is what I did. It works because

(x - 1)^2 - x^2 = 2x + 1

+6
Level 62
Jul 11, 2019
+3+5+7+9+11+13+15+17.......
+2
Level 50
Dec 29, 2019
1:15 left. Ez
+1
Level 25
Jun 5, 2020
ez dubs 1:07 left
+1
Level 25
Jun 5, 2020
27/30, I kept swearing as I shocked myself.

As I look at the list of answers, I see a pattern and I could now do this in half the time.

+1
Level 71
Jun 5, 2020
6 = 36 7 = ( 6+36+7) ........ 49
+1
Level 59
Jun 30, 2020
1:31 left in first try
+1
Level 44
Jan 14, 2021
whatt!? No way!
+1
Level 55
Nov 24, 2020
Is this too easy? I got it in 32 seconds on first try
+1
Level 46
Jan 13, 2021
1:33 remaining first try.
+1
Level 60
Jan 13, 2021
You just need to add the odd numbers ;)
+1
Level 78
Jan 13, 2021
A method I had was look at what first digit will equal, look at what last digit will equal, guess numbers in the middle. Doesn't really work when you get to 4 digit answers though
+1
Level 49
Jan 14, 2021
After 15, I just put the last digit constant and changed the first two digits until I got it right.
+3
Level 59
Jan 14, 2021
I just realized that this can be solved by taking the first square and then adding the next *odd* number to it.

Example:

0x0=0 (it may not really be a square, but bear with me)

1x1 = 1 (previous answer + 1)

2x2 = 4 (previous answer + 3)

3x3 = 9 (previous answer + 5)

4x4 = 16 (previous answer + 7)

5x5 = 25 (previous answer + 9)

6x6 = 36 (previous answer + 11)

7x7 = 49 (previous answer + 13)

8x8 = 64 (previous answer + 15)

9x9 = 81 (previous answer + 17)

10 x 10 = 100 (previous answer + 19)

And so on. I'm NOT a math-minded person but love patterns and that is just too cool! :P

+1
Level 52
Jun 7, 2021
thank you so much
+1
Level 69
Dec 8, 2021
And if you combine knowing that each increment is roughly the size of the previous increment with working out the final digit (which is trivial), then you don't really need to do the addition precisely, just ballpark it, then guess the closest number with the right final digit. Worst case you need two guesses.
+1
Level 28
Aug 27, 2021
1st Try- Thanks.
+1
Level 77
Jan 31, 2022
You can go really fast on this by just knowing what each digit the answer will end in. 1=1, 2=4, 3=9, 4=6, 5=5, and so on. Then when you get to the higher numbers just jump up about 30 or 40 and put in the appropriate end digit. You can smash through this quiz in about a minute without too much trouble. :)
+1
Level 65
Feb 16, 2022
I can only go until 13, then a couple of easy ones like 20 and 30. I should have know 16^2 is 256 and maybe 25^2 is 625.
+1
Level 17
Feb 16, 2022
Got it with 4 seconds left
+1
Level 53
Mar 28, 2022
After 16, you start forgetting these....
+2
Level 62
Apr 5, 2022
as in after age 16 or after you square all the digits up to 16?
+1
Level 60
Mar 29, 2022
0:04 seconds left!
+1
Level 2
Aug 24, 2022
x² =(x-1)² Û1

1² =1

2² =11=4

3² =41=9

4² =91=16

...

+1
Level 2
Aug 24, 2022
x² =(x-1)² Û1

1² =1

2² =11=4

3² =41=9

4² =91=16

...

+1
Level 68
Dec 15, 2022
pelvic!
+1
Level 68
Dec 15, 2022
pelvic!
+1
Level 68
Dec 15, 2022
pelvis
+1
Level 68
Dec 15, 2022
pelvis! I like
+1
Level 61
Dec 7, 2023
I knew up to 16 off the top of my head, but I somehow got the rest in time which im proud of.
+1
Level 61
Dec 7, 2023
I knew up to 16 off the top of my head, but I somehow got the rest in time which im proud of.