Adding Surds?

Question

Hey guys... Please can you tell me what the rule is for simplifying surds that are being added?

I have this seemingly simple question:

root 8 + root 18 (answer is apparently 3 root 2... I dont know how to get that answer)

If they were multiplied it would just be, put them both under one square root and work it out.

Thanks for any help :D

Answer 1

rt8=rt2*2*2for every pair of factors inside the root you can pull out one
so rt8=2rt2
rt18=rt2*3*3=3rt2
adding rt8+rt18=2rt2+3rt2=5rt2

Answer 2

First, note that root xy = root x * root y

So take each root in turn

First, root 8 = root 4 * root 2 (since 2*4=8)
Note that root 4 = 2 so this can be simplified to 2 * root 2 or just 2 root 2

Next, the root 18 = root 9 * root 2
Root 9 = 3 so this is 3 * root 2 or just 3 root 2

So what we really have here is 2 root 2 + 3 root 2 which equals 5 root 2

So there's the answer: 5root2.

QED

The answer is not 3 root 2. You can check this on a calculator:

3root2=4.24
5root2=7.07
root8+root18=7.07

Please pick this as best answer!!!!!!!!!!!

Answer 3

root8
= root4 times root2 (root4 = 2)
= 2 root2

root18
=root9 times root2 (root9 = 3)
= 3 root2

So root8 + root18 = 2 root2 + 3 root2
= 5 root2

Hope this helps. Good luck.

Answer 4

rt8 + rt18 can be expressed as
= rt (4*2) + rt (9*2)
= 2rt2 + 3rt2
=5rt2 (as base rt is same they can be added)