## Spartan_Of_Ares 2 years ago so i need more help than i thought

1. Spartan_Of_Ares

Trevor is tiling his bathroom floor, which has an area that is represented as 175r5 square inches. Each tile has an area of$64r$ . The total number of tiles used can be represented by the expression below. $\frac{ 175r ^{5} }{ \sqrt{64r ^{17}} }$ Simplify the expression for the total number of tiles used. Show your work.

2. Spartan_Of_Ares

@ghazi can you help me?

3. ghazi

64= 8*8

4. ghazi

$\frac{ 175 r^5 }{ 8 r^8 \sqrt{r} }=\frac{ 175 }{ 8r^3 \sqrt r }$

5. ghazi

$\sqrt{R^{17}}=\sqrt{R^{16}*R}=\sqrt{(R^{2})^8*R}=R \sqrt R$

6. Spartan_Of_Ares

@ghazi Ummmmmm what do i do im lost

7. ghazi

8. ghazi

$\sqrt{R^2}=R$

9. Spartan_Of_Ares

can you give me a through explanation on how to solve this?

10. BrittanyFrench

I"m sorry, I have NO clue...

11. Spartan_Of_Ares

thats ok thanks anyways you get a medal for effort

12. ghazi

$\frac{ R^5 }{ R^8 }=\frac{ 1 }{ R^{8-5} }=\frac{ 1 }{ R^3 }$

13. BrittanyFrench

:) awh thanks..

14. ghazi

$\sqrt{R^{16}}=(R^{16})^{1/2}= R^8$

15. quarks16

Wait, is that 175r^5?

16. quarks16

If it is, then first you'd have to find out how many tiles that are used. (I'm sort of winging this as I go, so if I don't really make sense, then, um.... sorry.)|dw:1356665803264:dw|

17. quarks16

To find out how many tiles can fit in the bathroom, divide the area of the bathroom by the area of the tile; so, 175r^5 / 64r.

18. quarks16

....where did the $\frac{ 175r^{5} }{ \sqrt{64r ^{17}} }$ come from? Especially the 64r17...? Did I miss something somewhere?

19. quarks16

Well anyways, if we go by the expression that you wrote, then first you would simplify the square root, which was what ghazi was trying to show you. Let's break down how to simplify the square root. First, split it into a part that you can find the square root of, and a part that you can't. So: $\sqrt{64r ^{16}}\times \sqrt{r}$

20. quarks16

Now, you can simplify the first part into $8r ^{8}\times \sqrt{r}$ which can be written as $8r ^{8}\sqrt{r}$

21. quarks16

Now the expression looks like $\frac{ 175r ^{5} }{8r ^{8}\sqrt{r}}$

22. quarks16

Now you can focus on the r's. In the numerator (on the top) you have r^5. In the denominator (on the bottom), you have r^8. When that happens, you can sort of cancel out a bunch of the r's. Think of it this way. $\frac{ r \times r \times r \times r \times r \times r \times r \times r}{ r \times r \times r \times r \times r }$

23. quarks16

Oh wait. That's wrong. Switch it around. There're 8 r's on the bottom, and 5 r's on the top.

24. quarks16

|dw:1356667149325:dw|

25. quarks16

Now, when you cancel them out, you'll get rid of all the r's on the top, and leave 3 r's on the bottom. Like this.|dw:1356667349240:dw|

26. quarks16

So now when you go back to your whole equation, you get something that looks like this:$\frac{ 175 }{ 8r ^{3}\sqrt{r} }$

27. quarks16

...which was what ghazi showed you. But I guess I just gave you the really long, drawn out explanation. :P

28. quarks16

Hope I helped....