Question

Trevor is tiling his bathroom floor, which has an area that is represented as 117r4 square inches. Each tile has an area of square root of the quantity 9 r to the thirteenth power . The total number of tiles used can be represented by the expression below.
one hundred seventeen r to the fourth power, all over the square root of the quantity nine r to the thirteenth power

Simplify the expression for the total number of tiles used. Show your work

Answer 1

Alright...so firstly....what is the square root of 9?

Answer 2

3

Answer 3

Right...so we can bring that 3 out of the radical

\[\large \frac{117r^4}{3\sqrt{r^{13}}}\] like that...okay?

Answer 4

Now, we also know that r^13 can be broken up like:

\[\large r^{13} = r^9 \times r^4\] right?

Answer 5

well it would be 3r^6 sqrt r

Answer 6

I'm not sure what you mean...explain please :)

Answer 7

in the denominator, there is an exponent of 13, you could take one out which would leave r*r^12. The r^12 could be simplified to r^6 outside of the sqrt, leaving it 3r^6sqrt(r)

Answer 8

Great job! I was going to do it another way...which would have taken 1 more step...but yes good workaround :)

so now we just have

\[\large \frac{117r^4}{3r^6\sqrt{r}}\]

Now we can simplify by doing...117/3 = 39

ad r^4/r^6 = r^{4 - 6} = r^-2

so pretty much at the very end we can have

\[\large \frac{39r^{-2}}{\sqrt{r}}\] or\[\large \frac{39}{r^2\sqrt{r}}\]

if you still wanted to simplify the denominator you definitely can :)

Answer 9

ok thank you!

Answer 10

Anytime :)