8.5 Lesson on Multiplying Radicals

Multiplying Radicals

By Blake Jensen

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What is the radicand?

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The Rules of Radicals

Product Rule works both ways!

The result can be simplified!

Multiply the radicands together.

In order to do this, they must have the same index

We can multiply the radicands!

Math Response

Multiply the following, you do NOT need to reduce it
$$\sqrt[]{7}\cdot\sqrt[]{9}$$

Type answer here

Correct Answer: \sqrt{63}

Deg^°

Rad

1) Multiply first.
2) Any large numbers can be broken down to their factors

1) Rewrite it into factors.
2) Look for factors that are squares

Simplifying Radicals

Math Response

Simplify!

$$\sqrt[]{18}$$

Type answer here

Correct Answer: 3\sqrt{2}

Deg^°

Rad

Math Response

Multiply them then simplify! No need to reduce on this one.

$$\sqrt[]{3}\cdot\sqrt[]{30}$$

Type answer here

Correct Answer: 3\sqrt{10}

Deg^°

Rad

Math Response

This time multiply and reduce!

$$\sqrt[]{5}\cdot\sqrt[]{27}$$

Type answer here

Correct Answer: 3\sqrt{15}

Deg^°

Rad

Numbers on the outside....

Act as a coefficients!

We can reduce first then multiply if it makes it easier!

Numbers outside act as coefficients, numbers on the inside are still radicands.

Let's try one together!

Open Ended

Your turn!
Don't give me an answer, tell me how you would simplify the following

$$\sqrt[]{81}\cdot\sqrt[]{45}$$