1. Using Your Algebra Skills 9
Radical Expressions
Using Your Algebra Skills 9

2. Use a sheet of square dot paper and draw a square that is 1 by 1.
Draw in the diagonal.
Use the Pythagorean Theorem to find the length of the diagonal.
Did you say the diagonal was the ?

3. Use a sheet of square dot paper and draw a square that is 2 by 2.
Draw in the diagonal.
Use the Pythagorean Theorem to find the length of the diagonal.
Did you say the diagonal was the ?

4. Finding another name for
Remember that the diagonal inside a 1 x 1 square measures
How many of the orange diagonals fit on the green diagonal?
Another name for would be
You might notice that
It follows that

5. Use a sheet of square dot paper and draw a square that is 3 by 3.
Draw in the diagonal.
Use the Pythagorean Theorem to find the length of the diagonal.
Did you say the diagonal was the ?

6. Finding another name for
Remember that the diagonal inside a 1 x 1 square measures
How many of the orange diagonals fit on the green diagonal?
Another name for would be
Similarly

7. Extending the pattern
Use a sheet of square dot paper and draw a square that is 8 by 8.
Draw in the diagonal.
Without using the Pythagorean Theorem find the length of the diagonal.
How many segments fit on the diagonal of a 8 by 8 square?

8. Another Common Square Root
Use a sheet of isometric dot paper and draw a an equilateral triangle that is 2 units on each side.
Draw in an altitude.
Notice two right triangles are formed. How long is each part of the base?
Use the Pythagorean Theorem to find the length of the altitude.
The altitude is

9. Use the Pythagorean Theorem to find the length of the altitude.
Use a sheet of isometric dot paper and draw a an equilateral triangle that is 4 units on each side.
Draw in an altitude.
Notice two right triangles are formed. How long is each part of the base?
Use the Pythagorean Theorem to find the length of the altitude.
Did you get the altitude to be ?

10. Remember that the first altitude was . (Red Line)
How many times does the red altitude fit on the green altitude?
Therefore,

11. Use the Pythagorean Theorem to find the length of the altitude.
Use a sheet of isometric dot paper and draw a an equilateral triangle that is 6 units on each side.
Draw in an altitude.
Notice two right triangles are formed. How long is each part of the base?
Use the Pythagorean Theorem to find the length of the altitude.
Did you get the altitude to be ?

12. Draw in a large equilateral triangle whose side is an even number.
Find the length of all sides of the right triangle.

13. Use the Pythagorean Theorem to find the length of the altitude.
Use a sheet of isometric dot paper and draw a an equilateral triangle that is 4 units on each side.
Draw in an altitude.
Notice two right triangles are formed. How long is each part of the base?
Use the Pythagorean Theorem to find the length of the altitude.
Did you get the altitude to be ?

14. Study these equality statements to make some generalizations

15. What would be other names for each of the following?