Reducing+Radicals


 * TASK: Review your flashcard for radicals. Describe radical in your own words.**

There are two ways that we can reduce radicals. The first way is the way that we usually think of which is taking the square root of a number. For example:



All of the above examples are called **perfect squares** because when we take their square root we get a whole number as our answer. However, sometimes we cannot take the square root of a number because it doesn't come out to a whole number (they're not perfect squares). For example:



In that case, we can reduce the radical a different way. First we have to break them down into a factor pair in which one of the factors is a perfect square (has a while number square root).

If we look at 500, it's factor pairs are: 1 and 500, 2 and 250, 4 and 125, 5 and 100 Out of all of these factor pairs, 4 and 100 are perfect squares. We always choose the largest perfect square. Once we have this factor pair, we can break the radical down into this pair and we get:



We can break this apart so we get:



And since we know that the square root of 100 is 10, we can simplify this further to get our final answer:



Here's another **example**:



**TASK: In your own words, explain the steps for reducing radicals that are not perfect squares**.

**TASK: How do you decide which factor pair to break the number inside the radical down into?**

When we break down radicals and they can't be broken down any further (they have no more factors that are perfect squares), then we say that the radical is in //simplest radical form//.


 * What do we do if there's a number in front of the radical already?** For example: [[image:Reducing_Radicals_7.jpg]]

In this case, the 3 and the radical 20 are being multiplied (we know this because there's no sign in between them). Therefore, we break down the radical 20 as we did above and then multiply our answer by 3. We get:



**TASK: Open the document and complete the practice problems. **