# 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

Rationalize the denominator and simplify:

Explanation:

To rationalize a denominator, multiply all terms by the conjugate. In this case, the denominator is , so its conjugate will be .

So we multiply: .

After simplifying, we get .

### Example Question #4 : 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 #5 : 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 #6 : Non Square Radicals

Simplify:

Explanation:

To simplify , find the common factors of both radicals.

### Example Question #7 : 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 #8 : Non Square Radicals

Explanation:

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

### Example Question #9 : 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 #10 : 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.