2. Vocab Radical – symbol used to indicate a square root Radicand – the expression under the radical Perfect square – a number whose square root is an integer To simplify means to find another expression with the same value. It does not just mean to find a decimal approximation

3. Finding the square root of a number is the equivalent of “unsquaring” it. This is a term I made up – but it makes sense. Start with a length 3 ft Now square it – or make a square out of it! It’s area is 9 ft 2 – when you square 3 you get 9.

4. To unsquare a number, or find its square root, start with a square… Now unsquare it – or figure out how long each side is. 25 ft 2 Each side is 5 ft, the square root of 25 is 5.

5. Some squares are perfect…this means their square root (or side length) is an integer. The first ten perfect squares are: 1 4 9 16 25 36 49 64 81 100

6. Why are these perfect? 1 4 9 16 25 36 49 64 81 100 1 22 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 ==================== OR squareunsquare

7. You can estimate square roots by determining which “perfect square” they are closer to…. Is between & Since 11 is closer to 9 than it is to 16, I would estimate is about 3 Of course you can also use a calculator!

8. Simplifying radicals….this is in Chapter 11, but we won’t get to Chapter 11 and this is a great place to talk about it! To simplify means to find another expression with the same value. It does not just mean to find a decimal approximation…especially with radicals!

9. Let’s look at some radical properties! This might look easier with numbers… We can prove this one… 6 = 3 * 2

10. Here’s another radical property! This might look easier with numbers too We can prove this one using a calculator.

11. In order to simplify radicals, you look at the number under the radical aka the radicand, which isn’t perfect, and try to find perfection! 45 is NOT perfect, but it has a factor that IS perfect…9 Rewrite 45 as 9 * 5

12. The perfect squares aren’t always so easy to see…it can be helpful to make a list of them to refer to and use a calculator to check for perfect factors! Simplify :

13. It works the same way with variables! Rewrite x 3 as x 2 * x x 2 is a perfect square…its square root is x x 3 is NOT perfect, but it has a factor that IS perfect… x 2

14. Let’s try combining numbers and letters! Simplify : 1) 2) 3) 4) 5) 6)

15. 1) 12x 2 2) 3) 4) 90a 3 bc 2 5) 6)