What if you were asked to find the sum of and ? How could you combine these two terms so that you could add them? After completing this lesson, you'll be able to simplify radical terms and expressions like these.

### Watch This

CK-12 Foundation: Simplifying Radicals Review

### Guidance

In algebra, you learned how to simplify radicals. Let’s review it here. Some key points to remember:

- One way to simplify a radical is to factor out the perfect squares (see Example A).
- When adding radicals, you can only combine radicals with the same number underneath it. For example, cannot be combined, because 5 and 6 are not the same number (see Example B).
- To multiply two radicals, multiply what is under the radicals and what is in front (see Example B).
- To divide radicals, you need to simplify the denominator, which means multiplying the top and bottom of the fraction by the radical in the denominator (see Example C).

#### Example A

Simplify the radicals.

a)

b)

c)

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For each radical, find the square number(s) that are factors.

a)

b)

c)

#### Example B

Simplify the radicals.

a)

b)

c)

d)

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a) Simplify before adding:

b)

c)

d) the and the cancel each other out

#### Example C

Divide and simplify the radicals.

a)

b)

c)

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Rewrite all division problems like a fraction.

a)

b)

c)

Notice, we do not really “divide” radicals, but get them out of the denominator of a fraction.

CK-12 Foundation: Simplifying Radicals Review

### Guided Practice

Simplify the radicals.

1.

2.

3.

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Answers:
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1.

2.

3.

### Practice

Simplify the radicals.