# Algebra II : Non-Square Radicals

## Example Questions

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### Example Question #1 : Non Square Radicals

Explanation:

To solve this, remember that when multiplying variables, exponents are added.  When raising a power to a power, exponents are multiplied.  Thus:

### Example Question #2 : Non Square Radicals

Simplify by rationalizing the denominator:

Explanation:

Since , we can multiply 18 by  to yield the lowest possible perfect cube:

Therefore, to rationalize the denominator, we multiply both nuerator and denominator by  as follows:

### Example Question #3 : Non Square Radicals

Simplify:

Explanation:

Begin by getting a prime factor form of the contents of your root.

Applying some exponent rules makes this even faster:

Put this back into your problem:

Now, we can factor out  sets of  and  set of .  This gives us:

### Example Question #4 : Non Square Radicals

Simplify:

Explanation:

Begin by factoring the contents of the radical:

This gives you:

You can take out  group of .  That gives you:

Using fractional exponents, we can rewrite this:

Thus, we can reduce it to:

Or:

### Example Question #5 : Non Square Radicals

Simplify:

Explanation:

To simplify , find the common factors of both radicals.

### Example Question #6 : Non Square Radicals

Simplify:

Explanation:

To take the cube root of the term on the inside of the radical, it is best to start by factoring the inside:

Now, we can identify three terms on the inside that are cubes:

We simply take the cube root of these terms and bring them outside of the radical, leaving what cannot be cubed on the inside of the radical.

Rewritten, this becomes

### Example Question #7 : Non Square Radicals

Explanation:

Simplify both radicals by rewriting each of them using common factors.

### Example Question #8 : Non Square Radicals

Simplify:

Explanation:

In order to simplify this radical, rewrite the radical using common factors.

Simplify the square roots.

Multiply the terms inside the radical.

### Example Question #9 : Non Square Radicals

Simplify:

Explanation:

Break down the two radicals by their factors.

A square root of a number that is multiplied by itself is equal to the number inside the radical.

Simplify the terms in the parentheses.

### Example Question #10 : Non Square Radicals

Simplify, if possible:

Explanation:

The first term is already simplified.  The second and third term will need to be simplified.

Write the common factors of the second radical and simplify.

Repeat the process for the third term.

Rewrite the expression.

Combine like-terms.