Simplifying radicals?

Question

I have a couple of problems for simplifying radicals.. Can you explain how to do them please? Write in simple radical form.

radical 192

4radical 27 -radical 75

15/ radical 6

Thank you very much

Answer 1

I'm pretty iffy on radicals, but I'll try to help you out here.

Okay, I'll start with a simple example here. 28 isn't a perfect square, right? So, you have to find multiples of 28 that are. I'll use 4 and 7. You simplify radical 28 to radical 4 x radical 7. Then you simplify the radical 4 to 2, and you have 2 radical 7. Since seven is a prime number, you've simplified as far as you can.

Here's your first problem;

Radical 192

Radical 4 x Radical 48

2 Radical 48

2 (Radical 4 x Raadical 12)

2 x 2 radical 12

4 radical 12

4 radical 4 x radical 3

4 x 2 radical 3

8 radical 3

And that's your first answer.



#2
4 radical 27 - radical 75

4 (radical 9 x radical 3) -radical 75(I'm going to leave that only for now)

4 x 3 (radical 3) - radical 75

12 radical 3 - (radical 3 x radical 25)

12 radical 3 - (radical 3 x 5)

7 radical 3

And that's #2.

#3

15/radical 6

Already simplified as far as possible I think.

Those would be my answers. I hope they helped!

Answer 2

to simplify a radical, you have to figure out if the number in the radical is divisible by a perfect square. For example. radical 192= radical 64 times radical 3. radical 64 can be simplified to 8, and you cant simplify radical 3, so radical 192= 8 radical 3. hope that helped.

Answer 3

I put this answer on a GIF with the explanation so you can see it better with the radical signs and everything.. Good luck.

http://www.geocities.com/ddeity_inc/mathradicals.gif