One word problem

Question

One word problem

xochital · Answer

Trevor is tiling his bathroom floor, which has an area that is represented as 120r3 square inches. Each tile has an area of square root of the quantity 16 r to the ninth power. The total number of tiles used can be represented by the expression below.
$$\frac{ 120r ^{3} }{ \sqrt{16r ^{9}} }$$

anonymous · Answer

Are we trying to find r?

xochital · Answer

i have to simplify the expression for the total number of tiles used

anonymous · Answer

yes you are correct,divide the area of floor by area of one tile

anonymous · Answer

Your first step would be to multiply the top and bottom by the denominator to get rid of the square root in the denominator.

xochital · Answer

so multiply 120r^3 by sqrt of 16r^2?

anonymous · Answer

yes and the bottom as well which will leave the same value it just makes the bottom sqrt go away. after that it is really simple to simplify

anonymous · Answer

post what you have after the first multiplcation

xochital · Answer

i don't know how to multiply them and simplify tho

xochital · Answer

so wait would it be $$120r ^{3}\sqrt{16^{2}}$$

anonymous · Answer

almost here is a simpler example:
$$\frac{ 1 }{ \sqrt{2} }\times \frac{ \sqrt{2} }{\sqrt{2} }=\frac{ \sqrt{2} }{ 2 }$$

xochital · Answer

oh wait i'm sorry i messed this up! it's supposed to be 16 to the 9th power

xochital · Answer

so what is 120r^3 * sqrt of 16^9 simplified?

anonymous · Answer

You leave the top. But you forgot the bottom on the part you posted.

anonymous · Answer

The equation would be:
$$\frac{ 120r^3\sqrt{16r^9} }{ 16r^9}$$

anonymous · Answer

Now you just ignore the square root and simplify the other part as best you can.

xochital · Answer

how do i simplify it?

xochital · Answer

by dividing?

anonymous · Answer

yes :)

xochital · Answer

120/ 16 is 7.5

anonymous · Answer

just use the greatest common factor to simplify them

xochital · Answer

idk how to do that. i didn't learn it

anonymous · Answer

It is just the largest number they have in common, they are both even numbers so you could use a 2 to simplify it a little and keep doing that until one of the numbers is not even.

xochital · Answer

oh so 8?

anonymous · Answer

yes divide the top and bottom by 8 that would be the next step to simplify