Simplifying radicals: 7(square root)48x - 2(square root)75x

[caitlynbby007]

7(square root)48x - 2(square root)75x

I got the part where you find the factors of the 48 and 75, but I can't figure out what you do with the number you bring out of the radical.
Do you multiply it or add it?

 

[stapel]

7(square root)48x - 2(square root)75x

Is the above either of the following?

. . . . .7 sqrt[48] x - 2 sqrt[75] x

. . . . .7 sqrt[48 x] - 2 sqrt[75 x]

When you reply, please include a listing of all of your work and reasoning so far. Thank you!

Eliz.

 

[caitlynbby007]

It's 7 sqrt[48 x] - 2 sqrt[75 x]


I have that the factors of 75 are:

5&5, 3

And the factors of 48 are:

4&4, 3

I just don't know if I'm supposed to take the 5 and multiply it to the 2 like so:

10 sqrt[75 x]

Or if I'm supposed to add it to the number on the outside like this:

7 sqrt[75 x]

 

[pka]

\(\displaystyle 7\sqrt {48x} - 2\sqrt {75x} = 28\sqrt {3x} - 10\sqrt {3x} = ?\)

OR
\(\displaystyle 28S-10S=?\)

 

[caitlynbby007]

The first one, thank you!