Math Help - How do I simplify this?

1. How do I simplify this?

We are given this and asked to simplify, in the other questions the numbers have a common large denomenator that has a clean square root but in this one they do not. I have no examples to work with and I have a quiz tomorrow so I could really use an answer

2. Re: How do I simplify this?

Originally Posted by Rayzala
We are given this and asked to simplify, in the other questions the numbers have a common large denomenator that has a clean square root but in this one they do not. I have no examples to work with and I have a quiz tomorrow so I could really use an answer
Factor $245=5\cdot 7^2$ rewrite $\sqrt{245}=7\sqrt{5}$

You can use this to factor.

3. Re: How do I simplify this?

Originally Posted by Plato
Factor $245=5\cdot 7^2$ rewrite $\sqrt{245}=7\sqrt{5}$

You can use this to factor.
Okay but that is just for the third term.. what about the others? I'm not sure how this is supposed to come together.

For the first term I got: 80 = 5 . 16(or 4 squared)
Second term I got: 75 = 3 . 25 (or 5 squared)
Fourth term I got: 108 = 3 . 36 (or 6 squared)

Then I added up the like terms and got a final answer of:
-74 (square root of 3) - 80 (square root of 5)

Is this correct? I'm pretty much just guessing.. my text book has a bunch of ridiculously simple questions and nothing like this

4. Re: How do I simplify this?

Originally Posted by Rayzala
Okay but that is just for the third term.. what about the others? I'm not sure how this is supposed to come together. You got the right answer, and I doubt you were just guessing.

For the first term I got: 80 = 5 . 16(or 4 squared)
Second term I got: 75 = 3 . 25 (or 5 squared)
Fourth term I got: 108 = 3 . 36 (or 6 squared)

Then I added up the like terms and got a final answer of:
-74 (square root of 3) - 80 (square root of 5)

Is this correct? I'm pretty much just guessing.. my text book has a bunch of ridiculously simple questions and nothing like this
My goodness. Have a little confidence in yourself. Plato showed you the basic idea: first extract the perfect squares. And YOU grasped it. And yes, you add like terms.

$-\ 6\sqrt{80} + 2\sqrt{75} - 8\sqrt{245} - 14\sqrt{108} = -\ 6\sqrt{16 * 5} + 2\sqrt{25 * 3} - 8\sqrt{49 * 5} - 14\sqrt{36 * 3} =$

$-\ 6 * 4\sqrt{5} + 2 * 5\sqrt{3} - 8 * 7\sqrt{5} - 14 * 6\sqrt{3} = -\ 24\sqrt{5} - 56\sqrt{5} + 10\sqrt{3} - 84\sqrt{3} = -\ 80\sqrt{5} - 74\sqrt{3}.$

A radical is just a number to be treated like any other.