Dude I feel. OK so think of square roots as variables... You can't add or subtract them unless they're the same. It's like that; whatever is under the square root has to be the same. And right now 2x^8 and 2x^12 are NOT the same. So let's fix that first.
In order for something to go outside the square root, it needs to be a perfect square... Like x^2 or x^4 or x^(insert even number here). Let's work with the second term and see if we can somehow get that x^12 down to x^8.
X^12 can be written as x^4 * x^8 because if you multiply two terms with the same base (x), you can just add the exponents to get one exponent. So x^4 * x^8 = x^(4+8) = x^12
Once we've separated the second square root like that, we can separate the second term into
9* sqrt(x^4) * sqrt(2x^8) which simplifies to 9x^2 * sqrt(2x^8) because the square root of x^4 is x^2.
Now both the first and second term have 2x^8 under the square root and even better, whatever is on the outside are "like terms" as well.
Think of the square roots as just another variable like a (I'm also kinda lazy and don't feel like writing out square roots when I'm solving.)
24x^2a–9x^2a=15x^2a.
Putting the square root back in, we have
15x^2sqrt(2x^8). Now you can simplify what's under the square root. The square root of x^8 is x^4 so it's gonna leave the square root and be written as 15x^2*x^4sqrt(2).
Like we did before, x^2 and x^4 have the same base (x) so multiplying them gives us x^(2+4) which is x^6.
So the answer is 15x^6sqrt(2) which is choice A.
Hope this helps! Let me know if you have questions! :)
