1. To recognize and create equivalent radical expressions To square binomials with radical terms To use the distributive property with radicals To simplify expressions under a radical by factoring out a perfect square To revisit quadratic equations and parabolas

2. Place a piece of centimeter grid paper in your communicator. Collect a chart of the equivalent lengths

3. Draw a square that holds 4 square units. Inscribe another square inside the square by connecting the midpoints of each side of the original square. Find the area of the inscribed square. Find the length of the side of the inscribed square.

4. Approximate the length of the side of the inscribed square by lining a piece of centimeter grid paper along the edge of the inscribed square.

5. Draw a square that holds 16 square units. Inscribe another square inside the square by connecting the midpoints of each side of the original square. Find the area of the inscribed square. Find the length of the side of the inscribed square. How is this side related to the previous inscribed squares?

6. Draw a square that holds 36 square units. Inscribe another square inside the square by connecting the midpoints of each side of the original square. Find the area of the inscribed square. Find the length of the side of the inscribed square. How is this side related to the previous inscribed squares?

7. Draw a square that holds 64 square units. Inscribe another square inside the square by connecting the midpoints of each side of the original square. Find the area of the inscribed square. Find the length of the side of the inscribed square. How is this side related to the previous inscribed squares?

8. Draw a square that holds 9 square units. Inscribe another square inside the square by connecting points that are one unit from each corner of the original square. Find the area of the inscribed square. Find the length of the side of the inscribed square.

9. Draw a square that holds 36 square units. Inscribe another square inside the square by connecting points that are two units from each corner of the original square Find the area of the inscribed square. Find the length of the side of the inscribed square.

10. Draw a square that holds 81 square units. Inscribe another square inside the square by connecting points that are three units from each corner of the original square. Find the area of the inscribed square. Find the length of the side of the inscribed square.

11. Draw a square that holds 144 square units. Inscribe another square inside the square by connecting points that are four units from each corner of the original square. Find the area of the inscribed square. Find the length of the side of the inscribed square.

12. NameSimplified Name NameSimplified Name Study these lists to see if you can determine how they are equivalent.

13. Make a conjecture about another way to write each expression at the right. Choose positive values for the variables, and use your calculator to test whether your expression is equivalent to the original expression. Summarize what you’ve discovered about adding, multiplying, and dividing radical expressions.

14. Use what you’ve learned to find the area of each rectangle below. Give each answer in radical form as well as a decimal approximation to the nearest hundredth. hundredth.

15. Example B Rewrite this expression with as few square root symbols as possible and no parentheses. Use your calculator to check your answer.

17. Example C Rewrite each expression with as few square root symbols as possible and no parentheses.