There are two ways to simplify this problem:

Method 1:

Method 2:

We can set in the cube of a binomial pattern:

Rewrite the expression as a positive root and the negative root

Take the square root of the positive root:

To check the answer, square the square root:

should be what was inside the square root in the beginning.

It checks out, so the complex root is

The perfect square of 25 will go into 150

The square root of 25 is 5.

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

Remember that , so .

Substitute in for

Step 1: Split the into .

Step 2: Recall that , so let's replace it.

We now have: .

Step 3: Simplify . To do this, we look at the number on the inside.

.

Step 4: Take the factorization of and take out any pairs of numbers. For any pair of numbers that we find, we only take of the numbers out.

We have a pair of , so a is outside the radical.
We have another pair of , so one more three is put outside the radical.

We need to multiply everything that we bring outside:

Step 5: The goes with the 9...

Step 6: The last after taking out pairs gets put back into a square root and is written right after the

It will look something like this:

In order to find all the roots for the polynomial, we must use factor by grouping:

We will group the 4 terms into two binomials:

We then take the greatest common factor out of each binomial:

We can see now that each term has a common binomial as a factor:

In order to find the roots, we must set each factor equal to zero and solve: