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princessgloomy · Oct 15, 2007, 08:13 AM

I am very confused and would like this explained please:

How to simplify the radical expression of 18?

IllinoisChip · Oct 15, 2007, 08:52 AM

When you say "radical expression," do you mean: $\sqrt {18}$ ?

If so, then what you do is break the number 18 down to its prime factors, as follows:

18 = 2*3*3

From this you can see that the number 3 is squared , so you can take it out of the radical as follows:

$<br /> \sqrt {18}\ = \sqrt {2 \cdot 3 \cdot 3}\ =\ \sqrt 2 \cdot \sqrt{3^2} = 3 \cdot sqrt 2<br />$

Hope this helps.

princessgloomy · Oct 15, 2007, 09:56 AM

Yes that's exactly what I needed. Your explanation of how to do it was much easier then the books- thank you! :D

princessgloomy · Oct 15, 2007, 12:41 PM

Okay one last math question today:

Which is greater, the geometric mean or the arithmetic mean of 4 and 12. Explain.

What I don't get is the geometric answer comes out as a radical right? So how do compare it to the arithmetic mean?

ebaines · Oct 15, 2007, 02:10 PM

Originally Posted by princessgloomy

Which is greater, the geometric mean or the arithmetic mean of 4 and 12. Explain.

What I dont get is the geometric answer comes out as a radical right? So how do compare it to the arithmetic mean?

The geometric mean does turn out to be a radical - you're correct. But that's OK - there's nothing that says you can't compare an irrational number like $sqrt 5$ against a rational number like 2.2 to see which is greater. I suggest you do the calculation on a calculator and see which is larger. For example, if the numbers were 2 and 10, the arithmetic mean would be 6 and the geometric mean is $\sqrt {2 \cdot 10}\ =\ \sqrt {20}\ =\ 2 \cdot \sqrt 5\ =\ 4.4721...$ , so in this case the arithmetic mean would be greater. Now try it with 4 and 12 and see what you get.

princessgloomy · Oct 17, 2007, 12:13 PM

So for the geo. Mean of 4 and 12 I get 6.928

And the arithmetic mean I get 8, so it is the greatest?

ebaines · Oct 17, 2007, 12:20 PM

Yep - that's right. In fact, I think you'll find that the arithmetic mean is always greater than the geometric mean.