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
First submittedNovember 11, 2012
Times taken51,471
Rating4.39
2:00
Enter number here:
0
 / 30 guessed
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Integer
Square
1
1
2
4
3
9
4
16
5
25
6
36
7
49
8
64
Integer
Square
9
81
10
100
11
121
12
144
13
169
14
196
15
225
16
256
Integer
Square
17
289
18
324
19
361
20
400
21
441
22
484
23
529
Integer
Square
24
576
25
625
26
676
27
729
28
784
29
841
30
900
+5
Level 56
Dec 24, 2012
Got 'em all with 25 seconds left. Great quiz!
+2
Level 60
Dec 24, 2012
21/30 :)
+1
Level 58
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...
+5
Level 20
Dec 26, 2012
We all thankfully know what 1 squared would equal to.
+10
Level 77
Jun 23, 2014
Yet curiously we don't all know 2 squared.
+1
Level 60
Jan 13, 2021
lol yeah
+1
Level 54
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 41
Dec 28, 2012
26
+1
Level 21
Jan 28, 2013
only got 1-13, without using a calculator
+8
Level 79
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 67
Sep 25, 2019
That seems to take much more time, maybe usefull in higher numbers, like 97
+2
Level 59
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 43
Sep 25, 2013
Got 30 out of 30, with 0:14 left.
+2
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.
+1
Level 60
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 60
Jan 15, 2015
1:08 left
+7
Level 42
Jan 22, 2015
Pretty easy so long as you know the trick to just adding the last difference plus 2 every time.
+1
Level 62
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 39
Feb 6, 2015
Did it all in my head... 38s remaining
+1
Level 39
May 21, 2015
1 minute left no calculator XD
+1
Level 73
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.
+1
Level 59
Jul 5, 2015
Gotta love the image of squares that is used for this quiz.
+1
Level 59
Sep 8, 2015
Yay, 28 secs left, maths class really payed off!
+1
Level 36
Nov 27, 2015
30/30 with 50secs left.... Well chuffed
+1
Level 11
Apr 10, 2016
I got all the way up to 28^2=784 :)
+1
Level 90
Dec 11, 2016
1:05 left on the clock. And I was slow due to writting on laptop.
+1
Level 73
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 68
Jan 28, 2018
33 sec left
+2
Level 48
Aug 13, 2018
1:43 left on the clock. Stop bragging now.
+2
Level 66
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 68
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 52
Dec 29, 2019
1:15 left. Ez
+1
Level 20
Jun 5, 2020
ez dubs 1:07 left
+1
Level 27
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 51
Jun 30, 2020
1:31 left in first try
+1
Level 45
Jan 14, 2021
whatt!? No way!
+1
Level 47
Nov 24, 2020
Is this too easy? I got it in 32 seconds on first try
+1
Level 44
Jan 13, 2021
1:33 remaining first try.
+1
Level 56
Jan 13, 2021
You just need to add the odd numbers ;)
+1
Level 57
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 43
Jan 14, 2021
After 15, I just put the last digit constant and changed the first two digits until I got it right.
+1
Level 61
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 53
Jun 7, 2021
thank you so much