# Thread: Reduce/Expand squareroots and exponentiation

1. ## Reduce/Expand squareroots and exponentiation

Hi,

I've got an to assignment, to reduce/expand the following work:

(x3 + √12)2 + √4 * 12(1/2) * (x2a + 3 / x2a)

I've tried to reduce it in pieces.

(x3 + √12)2 = x6 - 4√3x3
√4 * 12(1/2) * (x2a + 3 / x2a) = 12 + 4√3x3

So in all, is it equal to:

x6 + 4√3x3 + 12 + 4√3x3

Which is equal to:

x6+ 8√3x3 + 12

Though, i'm not sure, that I'm doing it the right way, or if there is more I can do, than the following.

2. ## Re: Reduce/Expand squareroots and exponentiation

Originally Posted by JrAl
to reduce/expand the following work:

(x3 + √12)2 + √4 * 12(1/2) * (x2a + 3 / x2a)
I wish I could read your post. Not sure what is what.

Here are some guesses.
$\displaystyle (x^3+\sqrt{12})^2=x^6+2\sqrt{12}x^3+12$

$\displaystyle \sqrt{4}\sqrt{12}=4\sqrt{3}$

$\displaystyle \frac{x^{2a+3}}{x^{2a}}=x^3$

But I don't know what goes with what.

3. ## Re: Reduce/Expand squareroots and exponentiation

Isn't (x3 + √12)2 equal to x6 + 4√3x3 + 12?

I mean, 4√3x3 instead of 2√3x3.

4. ## Re: Reduce/Expand squareroots and exponentiation

Originally Posted by JrAl
Isn't (x3 + √12)2 equal to x6 + 4√3x3 + 12?

I mean, 4√3x3 instead of 2√3x3.
Yes $\displaystyle 2\sqrt{12}=4\sqrt{3}$

5. ## Re: Reduce/Expand squareroots and exponentiation

All right. Thanks :-)

So I get:

x6 + 4√3x3 + 12 + 4√3x3

Which is equal to x6 + 8√3x3 + 12 ?

Can I reduce that anymore?

6. ## Re: Reduce/Expand squareroots and exponentiation

Originally Posted by JrAl
All right. Thanks :-)

So I get:

x6 + 4√3x3 + 12 + 4√3x3

Which is equal to x6 + 8√3x3 + 12 ?

Can I reduce that anymore?
NO

7. ## Re: Reduce/Expand squareroots and exponentiation

Thank you for the help!