1. Do Now No Calculators! 15x + 3y 3xy –3a – b + 10
Get your homework and yellow sheet out on your desk for Ms. Taylor to check.
Simplify each expression.
1. 14x + 15y – 12y + x
2. 9xy + 2xy – 8xy
3. –3(a + b) +
Simplify. All variables represent nonnegative numbers. 4. 5. 6.
15x + 3y
3xy
–3a – b + 10
No Calculators!

2. Do Now
Get out your homework from last week(radicals HW)

3. Adding and Subtracting Radical Expressions

4. Add and subtract radicals.
We add or subtract radicals by using the distributive property. For example,
Radicands are different
Indexes are different
Only like radicals—those which are multiples of the same root of the same number—can be combined this way. The preceding example shows like radicals. By contrast, examples of unlike radicals are
Note that cannot be simplified.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide

5. Square-root expressions with the same radicand are examples of like radicals.

6. Like radicals can be combined by adding or subtracting the coefficients only!!!
Notice that you can combine like radicals by adding or subtracting the numbers multiplied by the radical and keeping the radical the same.

7. Combining like radicals is similar to combining like terms.
Helpful Hint

8. Adding and Subtracting Square-Root Expressions
Add or subtract. A.
The terms are like radicals. B.
The terms are unlike radicals. Do not combine.

9. Adding and Subtracting Square-Root Expressions
Add or subtract. C.
the terms are
like radicals. D.
Identify like radicals.
Combine like radicals.

10. Try This!
Add or subtract. a.
The terms are like radicals. b.
The terms are like radicals.

11. c. d. The terms are like radicals. Try This! Add or subtract.
Combine like radicals.

12. Sometimes radicals do not appear to be like until they are simplified!
Simplify all radicals in an expression before trying to identify like radicals.

13. Simplify Before Adding or Subtracting
Simplify each expression.
Factor the radicands prime factorizing.
Cross and Toss
Simplify.
Combine like radicals.

14. Simplify Before Adding or Subtracting
Simplify each expression.
Factor the radicands using prime factorizing.
Cross and Toss.
Simplify.
The terms are unlike radicals. Do not combine.

15. Simplify Before Adding or Subtracting
Simplify each expression.
Factor the radicands prime factorizing.
Cross and Toss.
Simplify.
Combine like radicals.

16. Try This!
Simplify each expression.
Factor the radicands using prime factorizing.
Cross and Toss.
Simplify.
Combine like radicals.

17. Try This!
Simplify each expression.
Factor the radicands prime factorize.
Cross and Toss.
Simplify.
The terms are unlike radicals. Do not combine.

18. Try This!
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.

19. Geometry Application
Find the perimeter of the triangle. Give the answer as a radical expression in simplest form.
Write an expression for perimeter.
Prime Factorize.
Cross and Toss.
Simplify.
Combine like radicals.

20. Try This!
Find the perimeter of a rectangle whose length is inches and whose width is inches. Give your answer as a radical expression in simplest form.
Write an expression for perimeter
l + l + w + w
Combine like radicals.
The perimeter is in.

21. Lesson Quiz: Part I
Add or subtract. 1. 2. 3.
Simplify each expression. 4. 5.

22. Lesson Quiz: Part II
6. Find the perimeter of the trapezoid. Give the answer as a radical expression is simplest form.

23. Let’s talk about Tutoring
Basketball is over, my tutoring is now Tuesday/Thursdays 2:15-3:15
Must be in my room by 2:30 or Ms. Taylor is leaving
It is not a class, if you have questions, want help on a certain topic, or simply want to work on your homework while your math teacher is in the room incase a question comes up that is fine

24. Homework
On the back of the Radical Homework page cross out numbers 11, 12, 13, 16, 17 & 18
The rest are due tomorrow!!
Remember QUIZ FRIDAY
Polynomials Test DUE FRIDAY!
Signed Progress Reports due FRIDAY
Wednesday for BONUS POINTS!!