1. Oct 20, 2011

### styxrihocc

Given that (√3)^7 + (√3)^5 + (√3)^3 + 42(√3) may be expressed as 3^κ,
find the value of κ

Now I know that (√3)^ 7 is the same as 3^3.5 so I have 3.5, 2.5 and 1.5 but i have no idea how to calculate 42 (√3). Please help :(

2. Oct 20, 2011

### eumyang

Factor out a square root of 3.
$(\sqrt{3})^7 + (\sqrt{3})^5 + (\sqrt{3})^3 + 42(\sqrt{3}) = \sqrt{3}(\text{...} + \text{...} + \text{...} + 42)$
The expression inside the parentheses will simplify nicely.

3. Oct 20, 2011

### styxrihocc

I'm sorry i don't get it, how is that supposed to solve the problem? would be great if you could explain in detail

4. Oct 20, 2011

### eumyang

Without giving it away, I am factoring out the greatest common factor. If you have a polynomial like this:
x4 - 3x3 - 11x2 + 33x

The GCF would be x, so factoring it out would give you this:
x(x3 - 3x2 - 11x + 33)

In the same way, the GCF of the expression you have is the sqrt root of 3, so factor it out. What is the resulting expression inside the parentheses?

5. Oct 20, 2011

### styxrihocc

√3(√3^6+√3^4+√3^2+42)
so how do i find κ?

6. Oct 20, 2011

### eumyang

Now simplify what is in the parentheses.
What is
$(\sqrt{3})^6$?
$(\sqrt{3})^4$?
$(\sqrt{3})^2$?

7. Oct 20, 2011

### styxrihocc

27+9+3+42 so 81 total...what now??

8. Oct 20, 2011

### eumyang

So you have
$81\sqrt{3}$
Write 81 as a power of 3.
81 = 3?
And you know that
$\sqrt{3} = 3^{1/2}$.
Put it all together...?

9. Oct 20, 2011

### styxrihocc

damn now i feel really stupid having asked the question because that makes perfect sense. thanks a lot man