Question

How can I memorize square roots 1-30?
I got the list from yahoo answers:


1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11² = 121
12² = 144
13² = 169
14² = 196
15² = 225
16² = 256
17² = 289
18² = 324
19² = 361
20² = 400
21² = 441
22² = 484
23² = 529
24² = 576
25² = 625
26² = 676
27² = 729
28² = 784
29² = 841
30² = 900




but any ideas/ways on how i could memorize them?
I need to know them by monday.

Answer 1

Look at the bright side, you don't have to memorize 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30

Answer 2

And I only know 1-13, 15-17, 20, 25, 30 anyway, I'm not sure why you'd want to know all of them. The ones I know got me through my math degree.

Answer 3

Agent is correct, memorize the right side of the equal sign, in that order. I guess it might help. Methods of memorizing vary through the student body. You have to find the method that's suitable for you.

Answer 4

okay.

Answer 5

You can look for patterns.
Also, knowing how to FOIL binomials helps.

Answer 6

NP, what do you mean?

Answer 7

Did you notice that all those square numbers differ from one-another by an odd number?

Answer 8

what do u mean?

Answer 9

Look at the first few squares: 0, 1, 4, 9, 16, 25
The difference between 0 and 1 is 1
The difference between 1 and 4 is 3
The difference between 4 and 9 is 5
and so on.

Answer 10

i see.

Answer 11

The pattern goes: +1, +3, +5, +7, +9, +11, +13, + ...
Always increasing by an odd number.

Answer 12

So let's say you forget what 13^2 is, but you remember that 12^2 = 144...

Answer 13

ah. okay. thanks for the tip.

Answer 14

that is a good way of trying to memorize them.

Answer 15

To find 13^2 from 12^2, find the 13th odd number (2*13-1 = 25)
144 + 25 = 169.
;-)

Answer 16

mhmmm, could you quiz me in a bit?

Answer 17

also, is there another pattern?

Answer 18

What I meant by FOILing binomials (this is something you learn in algebra, but can be used for arithmetic as well) is FOIL = First Outer Inner Last
So for, say, 16^2 --> think of it as (10+6)*(10+6)
First: 10*10 = 100
Outer: 10*6 = 60
Inner: 6*10 = 60 (same as the outer if you're squaring so just double up what you just got.
Last: 6*6 = 36
Add it all up: 100+120+36 = 256.

With practice, you can do this quickly in your head. You really only need to memorize the squares up to 10^2 (but you should memorize at least up to 20 or 25 if you can).

Answer 19

im in pre algebra

Answer 20

but thanks.

Answer 21

Then you at least know order of operations and distributive property - that's all that is.

Answer 22

I recommend making flash cards and practice mental arithmetic whenever you can.
Resist the temptation to reach for a calculator whenever you have some arithmetic to do.
Try it mentally first - if it takes you more than a few seconds and you start to forget your last calculation, then write it down.
Only if that fails should you use a calculator.

Answer 23

What I like to do for practice is to take a deck of cards - you can take out the face cards and aces, so you just have 2-10 - shuffle them and deal out two numbers and try to add them, subtract them, multiply them, and divide them as quickly as you can mentally, and then deal out two more . . . until you go through the whole deck.

Answer 24

Cliffs, ill be back in about 30 minutes. do you think you will still he online?

Answer 25

be*

Answer 26

Maybe. I'm about to get ready for bed, but if I'm off elsewhere, try tagging my name "@CliffSedge"

Answer 27

Ok,thanks.

Answer 28

see you cliffs.

Answer 29

ill log out for right now. then log back in when i am back.

Answer 30

@CliffSedge

Answer 31

What's up?

Answer 32

nothing much.

Answer 33

you?

Answer 34

About to go to bed.

Pop quiz:
(mentally, no pencil, no calculator)
find 40^2

Answer 35

160?

Answer 36

On the right track, but not quite.

Answer 37

4x4 16 add a 0

Answer 38

40=4*10
4*4=16
10*10=100

Answer 39

1600

Answer 40

Right, now look at 20^2 and 30^2 and see that they are done the same way.

Answer 41

okay.

Answer 42

400

Answer 43

This is a key strategy to be able to figure things out mentally an to help you memorize patterns.

Next example: Find 35^2, knowing that 35=30+5
(Remember, FOIL)

Answer 44

35x35

Answer 45

1825

Answer 46

Seems a little too big. How did you find that?

Answer 47

see, i do not understamd foil, because i haventnbeen taught that yet, so i attempted to do some quick multiplication.

Answer 48

That's fine. It just takes practice.
35*35 = (30+5)*(30+5)
Using distributive property:
= 30*30 + 30*5 + 30*5 +5*5
30*30 = 900
5*5=25
The 30*5 shows up twice, so just double that to 300, and the total is
900+300+25.

Answer 49

You'll only have to use this trick if you trying to mentally figure out squares which you've forgotten. For example, I can remember most squares up to 25, but sometimes I forget some, like 19^2 or 23^2, so I do FOIL in my head.
You should definitely strive to memorize all squares up to 16^2; get those down solid first - they're pretty easy. After that, work on 17^2 through 25^2.
Try the FOIL trick and the pattern of adding odd numbers along the way.
Once you have those, just practice once in a while, either with flash cards, or try to just name all the squares you can in order and see how high you can go.

Answer 50

cliffs, you'll have to excuse me - gotta go. thanks for helping out :)

Answer 51

Sure thing, me too. Have a good night, Rachel.

Answer 52

you too, cliffs.