1. Algebra Review Radical Expressions page 280
Essential Question
Can you solve an equation with a square root radical?

2. Simplifying Radicals
In the next chapters, work will be done with radicals, specifically square root radicals,
such as _____ or _____.

3. If n is a positive integer that is greater than 1 and
What is a RADICAL?
If n is a positive integer that is greater than 1 and
a is a real number then,
where n is called the index, a is called the radicand, and the symbol √ is called the radical.

4. Square Root - definition from Wikipedia
In mathematics, a square root (√) of a number x is a number r such that
r2 = x, or in words, a number r whose square (the result of multiplying the number by itself) is x. Every non-negative real number x has a unique non-negative square root, called the principal square root and denoted with a radical symbol as √x. For example, the principal square root of 9 is 3, denoted √9 = 3, because 32 = 3 × 3 = 9. If otherwise unqualified, "the square root" of a number refers to the principal square root: the square root of 2 is approximately
Square roots often arise when solving quadratic equations, or equations of the form ax2 + bx + c = 0, due to the variable x being squared.
Every positive number x has two square roots. One of them is √x, which is positive, and the other −√x, which is negative. Together, these two roots are denoted ±√x.
Square roots of integers that are not perfect squares are always irrational numbers: numbers not expressible as a ratio of two integers. For example, √2 cannot be written exactly as m/n, where n and m are integers.

5. Square Root - easy definition
A number that when multiplied by itself equals a given number.
Root
A number that, when multiplied by itself some number of times, equals a given number.

6. Perfect Squares Know these! 12 = 1 22 = 4 32 = 9 42 = 16 52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
132 = 169
142 = 196
152 = 225
Perfect Squares
Know these!

7. A RADICAL is in simplest form when …#1
No perfect square factor,
other than one,
is ________ the radical sign.
under

8. Use this property from algebra!

9. Example (a)

10. Example (b)

11. Example (1)

12. Example (2)

13. Example (3)

14. Example (4)

15. Example (5)

16. Example (6)

17. Example (7)

18. Example (8)

19. Example (9)

20. Example (13)

21. Example (14)

22. A RADICAL is in simplest form when …#2
No fraction,
is ________ the radical sign.
under

23. Use this property from algebra!

24. Example (a)

25. Example (b)

26. A RADICAL is in simplest form when …#3
No fraction,has a radical in the _________________.
denominator

27. Rationalizing the Denominator,
Use a method called …
Rationalizing the Denominator,
by using this pattern.

28. Example (a)
Multiplying by
1 does not
change it’s value.

29. Example (b)
Multiplying by
1 does not
change it’s value.

30. Example (a) - AGAIN!

31. Example (b) - AGAIN!

32. Example (10)

33. Example (11)

34. Example (12)

35. RADICALS must always be expressed in simplest form!
Why?
So you are able to recognize the patterns.

36. Can you solve an equation with a square root radical?
Assignment
Algebra Review on page 280
1 to 29 odd numbers
Assignment
Written Exercises on page 288
1 to 15 odd numbers
Be prepared for a quiz on Simplifying Radicals!
Can you solve an equation with a square root radical?