Radicals, Radical functions and rational exponents Help please

**kbryant05** · June 4th 2006, 12:07 PM

The algebraic expression: I am not sure how to type this on the computer but in the parenthesis is the square root of t+h - square root of t over h

15.92(square root of t + h - square root of t over h)
models the average rate of change in the percentage of households online from t years after 1997 to t + h years after 1997. Use the expression to solve this problem...

Let t=4 and h=2. Evaluate the expression to find the average rate of change in percentage of households online from 2001-2003 that is, between 4 years and 4 + 2, or 6 years after 1997.

**Quick** · June 4th 2006, 03:42 PM

Is the expression,
$15.92\left(\sqrt{t+h} - \sqrt{\frac{t}{h}} \right)$
or
$15.92\left(\sqrt{t+h} - \frac{\sqrt{t}} {h}\right)$

**kbryant05** · June 4th 2006, 03:44 PM

I wish I could do what you just did with the numbers but it is everything over h. Does that make sense?

**Quick** · June 4th 2006, 03:47 PM

$\frac{15.92\left(\sqrt{t+h} - \sqrt{t}\right)}{h}$
like this?
Also, do you need this in simplest radical form or decimal

**kbryant05** · June 4th 2006, 03:53 PM

Yes that is how it is written awesome job. Yes to have in simplest form. I have tried several times to get it to work and can't seem to get it yet to work out.

**kbryant05** · June 4th 2006, 04:21 PM

I am not sure if this helps at all but my book has a an average rate change of 3.6% but I am not getting it at all? I am lost on this whole radical stuff.

**Quick** · June 4th 2006, 04:44 PM

$\frac{15.92\left(\sqrt{t+h} - \sqrt{t}\right)}{h}$
$\frac{15.92}{h}\left(\sqrt{t+h} - \sqrt{t}\right)$
$\frac{15.92}{2}\left(\sqrt{4+2} - \sqrt{4}\right)$
$7.96\left(\sqrt{6} - \sqrt{4}\right)$
$\sqrt{63.3616}\left(\sqrt{6} - \sqrt{4}\right)$
$\sqrt{63.3616}\sqrt{6} - \sqrt{63.3616}\sqrt{4}$
$\sqrt{63.3616\cdot6} - \sqrt{63.3616\cdot4}$
$\sqrt{380.1696} - \sqrt{253.4464}$
$\sqrt{96\cdot3.9601} - \sqrt{64\cdot3.9601}$
$\sqrt{96}\sqrt{3.9601} - \sqrt{64}\sqrt{3.9601}$
$\left(\sqrt{96}-\sqrt{64}\right)\left(\sqrt{3.9601}\right)$
$\left(\sqrt{16\cdot6}-8\right)\left(\sqrt{3.9601}\right)$
$\left(4\sqrt{6}-8\right)\left(\sqrt{3.9601}\right)$

Considering I'm not even in high school, this is as far as I could get without going insane. Maybe Black or Hacker could get you farther.

**kbryant05** · June 4th 2006, 04:47 PM

Oh my goodness I am so sorry I meant when I said everything being over h it was supposed to be the parenthesis only and the 15.92 on the side. I am so very sorry. I feel horrible.

**Quick** · June 4th 2006, 04:50 PM

That's okay, but is this the real expression?
$15.92\left(\frac{\sqrt{t+h}-\sqrt{t}}{h}\right)$

**kbryant05** · June 4th 2006, 04:52 PM

I can't express how sorry I am. Thank you for helping me.

**Quick** · June 4th 2006, 04:59 PM

Actually, it doesn't matter, because all three of these are the same thing.
$\frac{15.92}{h}\left(\sqrt{t+h} - \sqrt{t}\right)$

$\frac{15.92\left(\sqrt{t+h} - \sqrt{t}\right)}{h}$

$15.92\left(\frac{\sqrt{t+h} - \sqrt{t}}{h}\right)}$

So my answers the same, sorry I couldn't finish helping you.

**kbryant05** · June 4th 2006, 05:45 PM

Thank you for trying. i hope someone else can try to do it too.

**malaygoel** · June 4th 2006, 07:38 PM

Originally Posted by Quick

$\frac{15.92\left(\sqrt{t+h} - \sqrt{t}\right)}{h}$
$\frac{15.92}{h}\left(\sqrt{t+h} - \sqrt{t}\right)$
$\frac{15.92}{2}\left(\sqrt{4+2} - \sqrt{4}\right)$
$7.96\left(\sqrt{6} - \sqrt{4}\right)$
Considering I'm not even in high school, this is as far as I could get without going insane. Maybe Black or Hacker could get you farther.

well done, Quick
just substitute the value of 6^(1/2) and you will get the answer

**kbryant05** · June 4th 2006, 07:44 PM

This is what I have tried to do to come up with 3.6% but am off still??

15.92 (√ t + h -√ t)
h

15.92 (√ 4 + 2 - √ 4)
2
15.92 (√ 6 - √ 4)
2
√ 3.99 √ 6 - √ 3.99 √ 4
√3.99 * 6 - √ 3.99 * 4
√23.94 - √15.96 = √7.98/2 = 3.9

**malaygoel** · June 4th 2006, 09:07 PM

Originally Posted by kbryant05

This is what I have tried to do to come up with 3.6% but am off still??

15.92 (√ t + h -√ t)
h

15.92 (√ 4 + 2 - √ 4)
2
15.92 (√ 6 - √ 4)
2

7.96(2.4494 - 2)
= 7.96 * 0.4494
=3.577

Thread: Radicals, Radical functions and rational exponents Help please

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