### All Algebra II Resources

## Example Questions

### Example Question #21 : Understanding Radicals

Evaluate:

**Possible Answers:**

**Correct answer:**

Evaluate each square root. The square root of a number evaluates into a number which multiplies by itself to achieve the number in the square root.

Substitute the terms back into the expression.

The answer is:

### Example Question #22 : Understanding Radicals

Solve:

**Possible Answers:**

**Correct answer:**

Solve each radical. The square root determines a number that multiples by itself to equal the number inside the square root.

Rewrite the expression.

The answer is:

### Example Question #21 : Radicals

True or false: is a radical expression in simplest form.

**Possible Answers:**

False

True

**Correct answer:**

False

A radical expression which is the th root of a constant is in simplest form if and only if, when the radicand is expressed as the product of prime factors, no factor appears or more times. Since is a square, or second, root, find the prime factorization of 52, and determine whether any prime factor appears two or more times.

52 can be broken down as

and further as

The factor 2 appears twice, so is not in simplest form.

### Example Question #21 : 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 #2 : Non Square 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 #3 : Non Square 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 #4 : Non Square 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 #22 : 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 #6 : Non Square 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 #7 : Non Square 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:

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