How to divide irrational numbers?

Many times students just accept what they are told in math class without much questions; it's perhaps boring, they don't want to take time to investigate and delve deeper, or whatever the reasons.

The teacher feeds them with knowledge and they take it in: "Oh, okay, there's such a thing as Pi. Oh, okay, some numbers are irrational."

But a question such as this shows that the person is wondering, wanting to understand the material more. So it's a good question!

I will divide the 'division' question to two parts.

1) When exact answer is desirable, often we do cannot technically divide. For example, let's take Pi ÷ 2. Well, we just write it as Pi/2 or π/2 and leave it at that.

If we can simplify the answer, we do that. For example, √15/√5 can be simplified to √3.

We could simplify √2/2 this way: since 2 = √22, then √2/2 = √2/(√22) = 1/√2.

But often the expression √2/2 is left as is, since there is a convention that we should consider a root in the numerator to be "prettier" than a root in the denominator. Or I don't know why it is; I just remember this little rule from school math.

2) When you need a numerical answer, then you use the decimal approximation of the irrational number, and divide normally as you would decimals.

For example, to find Pi/2, you take the decimal approximation to Pi as, say, 3.14159, and go 3.14159 ÷ 2 = 1.570795.

Comments

Anonymous said…
Just wandered onto your blog, and saw this post -- one of the reasons for rationalizing the denominator, as far as I know, involves the fact that when computing with a slide rule, it's much easier to handle a radical in the numerator. At least, that's what my mother said.
Anonymous said…
the convention for leaving a irrational in the numerator comes from the days before calculators. It was a more accurate answer to do the long division with the irrational as the numerator, then you can approximate to the number of desired decimal places.

Popular posts from this blog

Logarithms in a nutshell

Saxon Math is not for everyone