Start by putting each term in terms of .

 is already in terms of  so leave it alone.

Notice that  can be rewritten as . Thus .

Next, notice that  can be rewritten as . Thus .

Now, add these terms together.

To determine which two consecutive integers flank  out of the set , square each number. The squares of each number in the set are:

;

it follows that

or

.

This is the correct choice.

Start by simplifying each radical.

Now each radical is in terms of .

Add them together.

Start by simplifying each radical:

Notice that each radical simplifies down into a multiple of . Now add up these values to simplify.

The square root of an integer is a rational number if and only if the radicand - the number under the symbol - is itself a perfect square. Of the integers under the four square roots given, only 9 is a perfect square, being equal to . The other three numbers are therefore irrational. 

When simplifying a square root, you must break up what's inside the square root into its simplest factors. For example  would break up to . Once you do that, you look for pairs of numbers. For each pair, you pull out the common number to the outside of the square root and leave whatever is left over inside the square root. So, for , you would break that up to  and then . As you can see, there is a pair of , so you pull out a  and leave whatever is left inside. Since the  is left over you would leave that inside the square root. So, you have a  outside the square root and a  inside the square root, which gives you .

In order to solve for , we need to move all of the variables on its side of the equation over to the other side of the equation.

We can see that our  is hiding in a square root, so in order to get the  out we will need to square the whole equation.

Because we're multiply a power of  with the power of , the two can multiply together to create a power of 

We can't do anything else to this equation as there are no like variables.

Our answer is 

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