1. Homework Solution lesson 8.5
9) X = 12 10) y=− ) n = 0 12) M = -3 13) Z = 8 14) T = 5

2. Homework
Lesson 8.7_page 533 #14-19 ALL

3. Lesson 8.7 Simplifying Radical Expressions

4. Properties of Radicals
For any real number a,
𝑛 𝑎 𝑛 = 𝑎 𝑖𝑓 𝑛 𝑖𝑠 𝑎 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑒𝑣𝑒𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟,
𝑎𝑛𝑑
𝑛 𝑎 𝑛 =𝑎 𝑖𝑓 𝑛 𝑖𝑠 𝑎 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑜𝑑𝑑 𝑖𝑛𝑡𝑒𝑔𝑒𝑟
EXAMPLE:
(−3) 2 = −3 =3
3 (−3) 3 =−3

5. Examples
49 𝑥 2 𝑦 5 𝑚 6
Answer: 7 x 𝑦 2 |𝑚 3 | 𝑦

6. STRUCTURE
You can write an expression with rational exponent in radical form
= = 5 16

7. Rewrite each expression in radical form
(6) 3 2
(7𝑦) 1 4
(2 𝑟 2 ) 4 5

8. Radicals - definitions
The definition of is the number that when multiplied by itself 2 times is x.

9. Simplifying radicals 1, 4, 9, 16, 25, 36, 49, 64, 81, 100…
Most numbers are not perfect squares, but may have a factor(s) that is (are) a perfect square(s).
The perfect squares are:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100…
Simplify the radical expression by factoring out as many perfect squares as possible:
48 = = =

10. Simplifying radicals 1, 8, 27, 64, 125,… 3 48 = 3 125 = 3 100 =
The perfect cubes are:
1, 8, 27, 64, 125,…
Simplify the radical expression by factoring out as many perfect squares as possible:
3 48 = = =

11. Try these - simplify:
If a radical has a perfect square factor, then we can pull it out from under the sign.
Ex:

12. Warm-Up #
Solve the equation by using the LCD. Check for extraneous solutions.
Simplify
𝟐𝒙 𝒙+𝟑 −𝟏= 𝒙 𝒙+𝟑

13. Homework Solution lesson 8.7
14) ) ) − ) ) 4x 2𝑥 19) 3x 2 𝑥

14. Homework
Lesson 8.7 page 534 #45-56 ALL

15. Lesson 8.7 Adding, Subtracting, and Multiplying Radical Expressions

16. Combining like-terms
3x+2x – 2
(3+x) + (3 + x)
(4 + n) –(-1 -3x)

17. Adding or Subtracting Radicals
To add or subtract square roots you must have like radicands (the number under the radical).
Sometimes you must simplify first:

18. TRY THESE:

19. Multiplying Radicals
You can multiply any square roots together. Multiply any whole numbers together and then multiply the numbers under the radical and reduce.

20. TRY THESE:

21. Warm-Up #
Simplify
4 250
− −
(3+ 2 ) 2

22. Homework Solution lesson 8.7
45) ) 7− 7 47) 2− 2 48) − ) −1− ) −5+15 5
51) −12− 3
52) −1−7 5
53) 1+ 3
54) 23−25 5
55) 12−10 3
56) 34−16 5

23. Lesson 8.7 page 533 #35-37 ALL #82-84 ALL
Homework
Lesson 8.7 page 533 #35-37 ALL #82-84 ALL

24. Lesson 8.7 Dividing and Rationalizing Radical Expressions

25. Dividing Radicals
To divide square roots, divide any whole numbers and then divide the radicals one of two ways:
1) divide the numbers under the radical sign and then take the root, OR
2) take the root and then divide. Be sure to simplify. or

26. YOU TRY

27. Converting Back and Forth
Convert from exponential to radical form:
(3) 1/3
(32𝑦) 4/3
Converting from radical to exponential:
4 (3𝑚) 2 8𝑟

28. Example
(64 𝑦 7 ) 𝑦 3

29. Rationalizing Radicals
It is good practice to eliminate radicals from the denominator of an expression.
For example:
We do not want to change the value of the expression, so we need to multiply the fraction by 1. But “1” can be written in many ways…
We need to eliminate
Since
we will multiply by one where

30. YOU TRY