i need help with adding radicals?

Question

okay so 4√8-2√50-5√72

Answer 1

Factor EVERY RADICAND down to where there are as many PERFECT SQUARE factors as possible.  

That is, replace 8 by 4•2, replace 50 by 25•2, replace 72 by 36•2.

 

Then take the square roots of each of those perfect square factors...then every one of these three original terms (involving radicals) will be in the form of an integer coefficient times square root of 2, and you can combine these 'like' terms.

Answer 2

Alright, Jared, let's do this.

 

The easiest way for me is to break down what's under the radical sign into its prime factors.

 

4√(2x2x2) - 2√(2x5x5) - 5√(2×2×2×3×3)

 

Now, every pair under the radical comes out front as just that single number. Whatever remains stays under the radical and gets remultiplied if necessary.For example, 2√(3x3x5x7) = (2x3)√(5x7) = 6√35.

 

Back to our problem...

 

(4x2)√2 - (2x5)√2 - (5x2x3)√2

 

Let's multiply...

 

8√2 - 10√2 - 30√2

 

Hey, getting close! Now, just like 2s - 4s = -2s, so we can combine like terms with all of our √2s. Our final answer is -32√2.

 

Hope this helps!