### All Algebra II Resources

## Example Questions

### Example Question #24 : Understanding Radicals

**Possible Answers:**

**Correct answer:**

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

### Example Question #25 : Understanding Radicals

Simplify by rationalizing the denominator:

**Possible Answers:**

**Correct answer:**

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 #26 : Understanding Radicals

Rationalize the denominator and simplify:

**Possible Answers:**

**Correct answer:**

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 #27 : Understanding Radicals

Simplify:

**Possible Answers:**

**Correct answer:**

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:

Returning to your radical, this gives us:

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

### Example Question #28 : Understanding Radicals

Simplify:

**Possible Answers:**

**Correct answer:**

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 #21 : Understanding Radicals

Simplify:

**Possible Answers:**

**Correct answer:**

To simplify , find the common factors of both radicals.

Sum the two radicals.

The answer is:

### Example Question #30 : Understanding Radicals

Simplify:

**Possible Answers:**

**Correct answer:**

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 #31 : Understanding Radicals

Simplify the radical:

**Possible Answers:**

**Correct answer:**

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

Multiply the two radicals.

The answer is:

### Example Question #32 : Understanding Radicals

Simplify:

**Possible Answers:**

**Correct answer:**

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

Simplify the square roots.

Multiply the terms inside the radical.

The answer is:

### Example Question #33 : Understanding Radicals

Simplify:

**Possible Answers:**

**Correct answer:**

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.

The answer is: