Radicals-getting a rational denominator

[liz777]

So one of my problems is the square root of 768/square root of 384. I tried multiplying it by the square root of 384/square root of 384, but i ended up with a crazy answer. Should I simply the radicals first and then try it?...never mind, I divide radical 768/radical 384 to get radical 2, right?

But another one I'm stuck on...how do you simplify 9/ square root of 448?

Also,if I have radical 324/radical 147, should I simplify it, like make radical 324, 2 radical 6?

 

[cepheid]

You need to prime factor 448 to see how this can be simplified. The most obvious first step is to recognize that 448 is even and divisible by 2 (by 4, in fact). If you do that you'll notice that the answer is also divisible by two, and so is the result of that division, and so on...in the end you'll find that 448 is divisible by 2 six times, with the result being 7.

448 = 64 x 7 = 2^6 x 7

of course the square root of 2^6 is 2^3 (ie the square root of 64 is 8). Can you proceed from this point?

 

[liz777]

Thanks, I think I get it. So if I simplied radical 448 out, I would get 8 radical 7. So my final answer would be 9 radical 7 divided by 56.