Math question from an oldtimer?

Question

With all modern technical help in class today, would you still be able to calculate the square root, or maybe even the 3rd, if you only had a piece of blanc paper and a pencil?

Answer 1

Many professors nowadays are realizing this fact that some students are solely relying on calculators instead of learning the actual techniques to solve problems, and therefore some of them are not letting their students use calculators on tests or even in class at all in an effort to spur student learning.

However, to answer your question, yes there are people out there that still know how to compute radicals by hand.

Answer 2

Instead of lambasting our educational system, let's realize that most people never could do these calculations, and even those that could usually didn't. Before calculators were in everybody's hands, people would buy books of mathematical tables and look them up.

Technology hasn't made people dumber, it has allowed people who can't do math to hold jobs. Cash registers that tell how much change to give haven't CREATED people that can't make change, they were invented BECAUSE so many people couldn't do it and businesses needed more people in those positions than were able to do the math in their heads.

Could most people calculate a square root by pencil and paper? No. Why would they? Just to prove they can do it? There are so many more useful and relevant things to spend our time on in schools.

Answer 3

Yes. Any intelligent person could. However calculating roots is not too relevant anyways. I can say though that it likely hasnt been taught in most schools for 20+ years. If students out east are doing it then they are wasting their time.

It is not a skill relevant to any profession. One can simply get by being able to estimate the root or work with it algebraicly.

Let me ask you this, "When was the last time in your life you needed to calculate a root where estimation would not have sufficed?"

Answer 4

I could do it by brute force, i.e. pick something I think is close, calculate the 2nd or 3rd power, then iterate. I don't remember the equation to do it directly, and I forgot it immediately after I learned it, since it isn't useful, and my memory isn't very good.

I think in general all this computing power is making us dumber at math. I don't think that is such a problem for regular people, the problem is it is making mathematicians dumber at math. So they don't work hard to come up with an elegant solution, where they can brute force solve it with computers (like my square root example above.)

Answer 5

Sure. If my students are curious--or if they doubt that sqrt(2) is a "real" number in the sense that it is inaccessible except though some electronic magic--I show them how.

I take exception to the statement that there is no reason to learn such things. Anyone who's even done a little number theory knows that elegant and thought-provoking approximations to surds are everywhere in the subject, and many people are still tantalized by the way in which combinations of rationals try to merge into the mysterious infinite of irrationality.

Answer 6

Sure. I learned by doing the square roots by hand using the algorithm that is similar to long division. I also started with a slide rule and tables of trig functions and logarithms, so I guess I'm an old-timer also. Given enough time, I could probably make up a decent table of logs if you wanted me to.

Answer 7

Sure. I've done it in class. If you want to be one of the people who can do it, there's a link below that describes it very, very well.

But it does beg the question - if instructions on how to do it are written down somewhere, is it really important that people learn how to do it? I mean, how many people know how to spin thread on a spinning wheel? Such knowledge may concievably become useful under the right set of circumstances, but are those circumstances likely enough to be worth preparing for?

Answer 8

If you have the right teacher that can find balance in thechnology and the originally pencil and paper, but nowadays, sadly, this is a student speaking, no, we most likely couldn't do it because we weren't trained to work with pencils and paper, everything is digital now. =(

Answer 9

Sadly, the typical functional illiterate produced by the defective American school system, can not do even the most basic math problems.

Some time back, I bought a burger at a Burger King... the girl at the window handed me my change and said "your change is three seven ten"... "Huh"... "three seven ten"... "Do you mean THREE SEVENTEEN?"... "yeah... I guess"...

Somehow, I feel she was the best one in the math class.

Answer 10

There are a number of websites that show how to do them. Grab your favorite search engine and type in "square root algorithm" or "cube root algorithm." (Square roots are MUCH easier than cube roots, btw.)