In order to add or subtract, first simplify each radical completely. If the remaining number under the square root sign is the same for both numbers they can be added- much like with variables.

For this problem, it goes as follows:

In order to add, first simplify the first radical as follows:

Since the radicals are the same, treat them like variables and add the "coefficients" in from of them to solve.

Combine like terms:

Distribute:

Combine like terms:

In order to add or subtract, first simplify each radical completely. If the remaining number under the square root sign is the same for both numbers they can be added- much like with variables.

For this problem, it goes as follows:

In order to add, first simplify the first radical as follows:

Since the radicals are the same, treat them like variables and add the "coefficients" in from of them to solve.

Combine like terms:

Distribute:

Combine like terms:

The first two terms are already in simplified form because the number in the radical cannot be broken down into numbers that have pairs.

We will only need to break down the last term...

We then replace in the original equation with what we just calculated:

Add common terms, and then we have our final answer...

Which of the following is equivalent to ?

When dealing with fractional exponents, keep the following in mind: The numerator is making the base bigger, so treat it like a regular exponent. The denominator is making the base smaller, so it must be the root you are taking.

This means that is equal to the fifth root of b to the fourth. Perhaps a bit confusing, but it means that we will keep , but put the whole thing under.

So if we put it together we get:

Exponents raised to a power of <1 can be written as the root of the denominator.

So:

Recall that a square root can give two answers, one positive and one negative.

The first step is to factor both polynomials

becomes

Now we cancel out any terms that are in both the numerator and denominator. Remember that any variables/numbers that are in parenthesis are considered a single term.

In this case, the common term is

Simplified, the equation is: