Equations, Inequalities and VICs (3rd ed), Chapter 7

[nvingers]

In Action Problem 13:

In step 9 of the algebraic solution to this problem (as explained on the bottom of p. 156), we have a = c / rt c/d rt. In the next step, however, this all of a sudden becomes a = c / rt cd rt / d. Where does this come from? Why does c divided by the root of c over d all of a sudden become c divided by the root of cd divided by c?

Could somebody help me with this?

Thanks!

[StaceyKoprince]

When posting, please be sure to read (and follow!) the forum guidelines. Please post the full text of the problem (you do not need to post all or even part of the solution - unless, of course, you have a specific question about part of that solution).

Because we're a little bit behind and haven't gotten to your post in a while, I'll go ahead and answer today. But, in future, be warned: we're going to ask you to post the full text of the problem before we reply. :)

This is definitely an extremely challenging problem. The problem states:
a, b, c, and d are positive integers. If ab=c and a/b = d, what is a+b?

In solving for a, the problem offers:
a = c / [SQRT(c/d)]

We're not supposed to have square root signs on the denominators of fractions, so the problem takes the step of multiplying both the top and the bottom of the fraction by the same number: the denominator, SQRTd.

[SQRTc/SQRTd] * [SQRTd / SQRTd] = (SQRTc * SQRTd) / (SQRTd * SQRTd)
That last part simplifies: (SQRTd * SQRTd) = d
so the whole thing becomes: (SQRTcd)/d

The problem also does the same type of calculation a couple of steps later, when we find SQRTcd on the denominator of a fraction - both the top and bottom are multiplied by SQRTcd.