Last time we learned about radical expressions. Let's take a short review.

Find the principal square root.

After selecting your answer, click the “Submit” button.

Now, let's move on with today's lesson.

We know that <EQUATION>.

Therefore it’s a perfect square number.

The <EQUATION> is equal to the rational number <EQUATION>.

We can look at this expression a different way: <EQUATION>

Next, we can separate the two terms under their own radicals, so that we have: <EQUATION>

The <EQUATION> is <EQUATION>, and the <EQUATION> is <EQUATION>.

Again, we have arrived at the same conclusion: <EQUATION>

This is an example of the product property of square roots.

For any numbers a and b: <EQUATION>.

It is required that <EQUATION> and <EQUATION>

Look at this radical expression: <EQUATION>

Using the product property, we can write it as: <EQUATION>

What is this expression equal to? Click the “Submit” button after selecting your answer.

The <EQUATION> is <EQUATION>. The <EQUATION> is <EQUATION>.

Therefore, we have:<EQUATION>

Now, you try rewriting some radical expressions.

You are given a radical expression. Use the product property to rewrite it in simplest form.

Click the “Submit” button after selecting your answer.

Here we have the radical expression: <EQUATION>

At first, it may seem difficult to find the value of the square root.

However, we can rewrite this expression as: <EQUATION>

What is the value of this expression, written as a decimal? Click the “Submit” button after selecting your answer.

The <EQUATION> is <EQUATION>, and the <EQUATION> is <EQUATION>.

We find that: <EQUATION><EQUATION>.

This is an example of the quotient property of square roots.

It states that for any numbers a and b: <EQUATION><EQUATION>

Where <EQUATION> and <EQUATION>

Here we have the radical expression: <EQUATION>

What is this expression equal to? Click the “Submit” button after selecting your answer.

We find that: <EQUATION><EQUATION>

Remember that <EQUATION> must be a nonnegative number.

Therefore, our answer should have read: <EQUATION>

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