I'm one of those theoretical physicists who is notoriously bad at this, especially when there are nasty square roots etc.

Do you know of any techniques for increasing speed/accuracy other than attempting all the PGRE questions without a calculator.

Is there any software that can `train' you at this sort of stuff? My exam isn't until Oct '08, so I've got plenty of time.

## Mental arithmetic

- Kaiser_Sose
**Posts:**48**Joined:**Sun Sep 28, 2008 11:20 pm

### Re: Mental arithmetic

I used to be pretty poor at it as well. I am still not great. What helped me was tutoring lots of introductory/remedial algebra. Sounds painful I know but it has been more beneficial than not.

For square roots, I think the best thing is to know your perfect squares up to like (15)^2. Then when you have one that isn't a perfect square, you know the perfect roots it is likely in between.

For multiplication of stuff with double digits (or more) I just factor everything and then try to multiply.

Like 27 * 14 = (9*3)*(7*2)

I normally multiply the "hard" stuff (numbers bigger than 4 say) first because its easier to then double or triple it at the end.

So from above = (63)*3*2 = 189*2 = 378. Sounds elementary school, and it is, but I find it speeds me up quite a bit. Plus its great for scaring freshman algebra students when you have it from your head before they get it on their calculator. Never understood why some people think rote calculations in your head is more impressive than doing algebra or calc in your head. Hope that's helpful.

For square roots, I think the best thing is to know your perfect squares up to like (15)^2. Then when you have one that isn't a perfect square, you know the perfect roots it is likely in between.

For multiplication of stuff with double digits (or more) I just factor everything and then try to multiply.

Like 27 * 14 = (9*3)*(7*2)

I normally multiply the "hard" stuff (numbers bigger than 4 say) first because its easier to then double or triple it at the end.

So from above = (63)*3*2 = 189*2 = 378. Sounds elementary school, and it is, but I find it speeds me up quite a bit. Plus its great for scaring freshman algebra students when you have it from your head before they get it on their calculator. Never understood why some people think rote calculations in your head is more impressive than doing algebra or calc in your head. Hope that's helpful.

### Re: Mental arithmetic

people act like your a genius if you can solve a rubiks cube http://www.rubikssolver.com/.

I never will get it.

I never will get it.

### Re: Mental arithmetic

I learned from websites how to solve it and can do so easily now. However, I feel like anyone who has figured out how to do that thing without any outside help deserves to get into any grad school there iscato88 wrote:people act like your a genius if you can solve a rubiks cube http://www.rubikssolver.com/.

I never will get it.

This guy made a robot out of a Lego set that scans the cube and then solves it. Here's a video.

### Re: Mental arithmetic

Kaiser_Sose,

You have an interesting way of doing it. I would usually multiply things like that by breaking one of them into 10 + something, e.g.,

27*14 = 270 + 27*4 = 270 + 108 = 378.

I'm not very fast though.

I'm not sure I understand your technique with square roots. How would you approach e.g., sqrt(2.6) ?

You have an interesting way of doing it. I would usually multiply things like that by breaking one of them into 10 + something, e.g.,

27*14 = 270 + 27*4 = 270 + 108 = 378.

I'm not very fast though.

I'm not sure I understand your technique with square roots. How would you approach e.g., sqrt(2.6) ?

### Re: Mental arithmetic

http://en.wikipedia.org/wiki/Mental_calculation

I especially like the method for approximating square roots

I especially like the method for approximating square roots

- Kaiser_Sose
**Posts:**48**Joined:**Sun Sep 28, 2008 11:20 pm

### Re: Mental arithmetic

Ew sqrt(2.6) ?

In that case there's really two ways to think of it.

1.) Its gotta be bigger than one and less than two, by intuition. So a ballpark answer would be 1.5.

2.) You can get closer if you happen to know to sqrt(2) and sqrt(3), which are about 1.4 and 1.7 respectively. So a closer guess is probably 1.6.

This method works out more neatly is you have a larger number say, 53. The closest square roots are 49 and 64 which are 7^2 and 8^2 so you know that sqrt(53) is 7 and some change.

I tend to use your method, noospace, when confronted with multiplying decimals, like when I get an approximation from the above method.

Say I have 5*sqrt(53) ----> 5*(7.3) = 5*(7+0.3) = 35 + 1.5 = 36.5

Hope that's clear.

In that case there's really two ways to think of it.

1.) Its gotta be bigger than one and less than two, by intuition. So a ballpark answer would be 1.5.

2.) You can get closer if you happen to know to sqrt(2) and sqrt(3), which are about 1.4 and 1.7 respectively. So a closer guess is probably 1.6.

This method works out more neatly is you have a larger number say, 53. The closest square roots are 49 and 64 which are 7^2 and 8^2 so you know that sqrt(53) is 7 and some change.

I tend to use your method, noospace, when confronted with multiplying decimals, like when I get an approximation from the above method.

Say I have 5*sqrt(53) ----> 5*(7.3) = 5*(7+0.3) = 35 + 1.5 = 36.5

Hope that's clear.