## Example Questions

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Subtract and simplify:

Explanation:

Find the lease common denominator:

A radical cannot be in the denominator:

Find the value of .

Explanation:

To solve this equation, we have to factor our radicals.  We do this by finding numbers that multiply to give us the number within the radical.

4 is a perfect square, so we can find the root:

Since both have the same radical, we can combine them:

Simplify the following equation:

Cannot simplify further

Explanation:

When simplifying, you should always be on the lookout for like terms. While it might not look like there are like terms in , there are -- we just have to be able to rewrite it to see.

Before we start combining terms, though, let's look a little more closely at this part:

We need to "distribute" that exponent to everything in the parentheses, like so:

But 4 to the one-half power is just the square root of 4, or 2.

Okay, now let's see our equation.

We need to start combining like terms. Take the terms that include x to the one-half power first.

Now take the terms that have x to the one-third power.

All that's left is to write them in order of descending exponents, then convert the fractional exponents into radicals (since that's what our answer choices look like).

Simplify.

Explanation:

and

Plug in the simplified radicals into the equation:

which leaves us with:

Because these are not like terms, we cannot simplify this further.

Simplify.

Explanation:

Only the first two radicals can be simplified:

and

Plug in the simplified radicals into the equation:

We can now simplify the equation by combining the like terms:

Simplify.

Explanation:

We can simplify the first and third radicals:

and

Plug in the simplified radicals into the equation:

Combine the like terms:

Explanation:

Explanation:

The third root of  is

and when added to the square root of 64, which is 8, you should get 11.

Solve.

Explanation:

When adding and subtracting radicals, make the sure radicand or inside the square root are the same.

If they are the same, just add the numbers in front of the radical.

Since they are not the same, the answer is just the problem stated.

Solve.