In order to solve for , we need to have all the variables on one side that isn't . Lucky for us our only other variable, , is on the other side of the equation.

Our next step then is to make sure  is naked, meaning that there is nothing attached to our variable in order to solve it. We can see that our  is encased in a square root, so we will need to get it out of there first.

In order to get rid of the square root, we will need to square the entire equation. The square and square root will cancel each other, releasing the .

We can now stop, as there is nothing else we can do to this equation because  is the lowest we can go.

Our answer is 

In order to solve for , our first priority is to get all the variables to one side so that  is by itself. And luckily for us the problem already has all of the variables to to the other side.

Our next step then is to make sure  is naked, meaning that there is nothing attached to the . We can see that our  is not naked and is within a square root.

In order to get rid of the square root, we must square both sides of the equation The square root and square will cancel each other out, freeing the .

Since the right side of the equation needs to be squared, we have to foil  in order to properly distribute the square.

 can be also written as 

Foil the equation.

 and  can be classified as the same as it would be like writing  and , so we can combine the two.

Let's bring back our  since there is nothing more we can do to this equation.

Our answer is 

In order to solve for , we need to move all of the variables on its side over to the other side. We can see that our  is being squared. In order to get rid of that square, we will need to square root the whole equation, as the square and square root will cancel out.

Because this is a square root of , our  is like saying we have  's. A square root can divide to the power of  by , which leaves us with . The square root will also disappear for the  because it has divided it.

We cannot go any further into this equation as there are no like variables to put together.

Our answer is 

In order to solve for , we need to move all the variables beside it to the other side of the equation. Luckily for us  is all by itself.

Our next step then is to make sure  is naked, meaning nothing it attached to it. We can see though that our  is being squared, so we need to get rid of that in order to proceed.

In order to get rid of the square, we must square root the whole equation. The square root and square will cancel each other out.

Since we don't have any variables that are the same, this is as far as we can go.

Our answer is 

Start by simplifying each radical.

The radicals all simplify down into multiples of . You can add them together.

where

The numbers and fit those criteria. Therefore,

You can double check the answer using the FOIL method

Factor  all the way to its prime factorization.

 can be factored as the difference of two perfect square terms as follows:

 is a factor, and, as the sum of squares, it is a prime.  is also a factor, but it is not a prime factor - it can be factored as the difference of two perfect square terms. We continue:

Therefore, all of the given polynomials are factors of , but  is the correct choice, as it is not a prime factor.

 can be seen to fit the pattern 

:

where 

 can be factored as , so

 .

 does  not fit into any factorization pattern, so it is prime, and the above is the complete factorization of the polynomial. Therefore,  is the correct choice.

Divide termwise: