1. 3-8 Semester Math 2
Simplifying radicals

2. Do now 3/9

3. Good Things

4. Agenda Do Now Good Things! Notes: Exponent Rules Simplifying Radicals
Practice

5. Exponent Rules

6. Exponent Rules Simplify: (n2)3 Simplify: (x5)7
“Power to Power” Rule: multiply the exponents
Simplify: (n2)3
Simplify: (x5)7

7. Exponent Rules Simplify: (x5)(x7)
Multiplying Rule: add the exponents IF THEY HAVE LIKE BASES
Simplify: (x5)(x7)

8. Exponent Rules

9. Exponent Rules

10. Your Turn! Take 3 minutes to do as many as you can before we review
4. (x-3) 6.
2. (x7)2 5.
3. (m6)(m2)

11. Simplifying radicals
If the index is not written, it is automatically a 2

12. Perfect Squares 9 16 25 49 64
Today we will be working with numbers that are not perfect squares

13. Simplifying radicals
1. Write the prime factorization of the radicand (Factor tree)
2. Determine index of radical
3. Circle groups of numbers based on index and pull out ONE number from each group
Ex: if index is 2, circle groups of 2
Ex: if index is 3, circle groups of 3
4. Leave anything not circled under the radical
5. Multiply numbers & variables outside the radical together

14. Prime factorization
√75 5 15 2 8 5 3 2 4
5√3 2 2
2√2

15. Partner practice
Simplify: √40
Simplify: √54

16. Spot the mistake Simplify: √18 Simplify: √18 2 9 3√2 2√3 2 9 3 3 3 3
One of these is done correctly. One of these is wrong. Turn and talk – identify which one is wrong and WHY it is wrong.
Simplify: √18
Simplify: √18 2 2 9 9 3 3 3 3
3√2
2√3

17. Spot the mistake Simplify: √125 Simplify: √125 5 25 5√5 5 5 25 5 5 5 5
One of these is done correctly. One of these is wrong. Turn and talk – identify which one is wrong and WHY it is wrong.
Simplify: √125
Simplify: √125 5 5 25 25 5 5 5 5
5√5 5

18. Switching Forms

19. Exponent Over Index cv cv cv

20. Exponent Over Index

21. Exponent Over Index

22. Partner Practice Front: Simplifying Radicals
Back: Switching from radical to exponent form
Solution station at the front!