1. Simplifying Radicals
Section 10-2 Part 2

2. Goals Goal Rubric To simplify radicals involving quotients.
Level 1 – Know the goals.
Level 2 – Fully understand the goals.
Level 3 – Use the goals to solve simple problems.
Level 4 – Use the goals to solve more advanced problems.
Level 5 – Adapts and applies the goals to different and more complex problems.

3. Vocabulary
Rationalize the Denominator

4. Simplest Form

5. Simplifying Radicals Simplifying Fractions within radicals
The radicand has no fractions.
Simplifying Radicals Simplifying Fractions within radicals

6. Dividing Radicals

7. Example: Simplifying Fractions Within RadicalsB.
Simplify.
Quotient Property of Square Roots.
Quotient Property of Square Roots.
Simplify.
Simplify.

8. Your Turn: Simplify. a. b. Quotient Property of Square Roots.

9. Your Turn: Simplify. Quotient Property of Square Roots.
Factor the radicand using perfect squares.
Simplify.

10. Example: Simplifying Radicals with Quotients
Quotient Property.
Product Property.
Write 108 as 36(3).
Simplify.

11. Example: Simplifying Radicals with Quotients
Quotient Property.
Product Property.
Simplify.

12. Your Turn: Simplify. Quotient Property. Product Property.
Write 20 as 4(5).
Simplify.

13. Your Turn: Simplify. Quotient Property. Product Property. Write as .

14. Your Turn:
Simplify.
Quotient Property.
Simplify.

15. Simplifying Radicals Rationalizing Denominators
No radicals appear in the denominator of a fraction.
Simplifying Radicals Rationalizing Denominators

16. Definition
Rationalize the Denominator – the process of removing a radical from the denominator of a fraction.
A quotient with a square root in the denominator is not simplified. To simplify these expressions, multiply by a form of 1 to get a perfect-square radicand in the denominator. This is called rationalizing the denominator.
Why - It is easier to work with radical expressions if the denominators do not contain any radicals.

17. Rationalizing the Denominator
The process of multiplying the top and bottom of a radical expression by a form of 1to make the denominator a perfect square is called rationalizing the denominator.
Any number divided by itself is 1. Multiplication by 1 does not change the value of the expression.
The denominator contains no radicals, we have rationalized the denominator.

18. Example: Rationalize Denominator
Notice what we multiplied by to get rid of the square root
of 2 in the denominator.
When we multiply a square root by itself we get an answer
containing no radicals. For monomial denominators
containing square roots, your choice for multiplication can
just be that square root over itself. But you should simplify
first as we did here – or your problem may be
messier than it needs to be.
The denominator contains no radicals, we have rationalized the denominator.

19. Example: Rationalizing the Denominator
Factors of 56.
Simplify denominator.
Multiply numerator and denominator by the denominator
Take square root of 4 and write it outside the radical sign
Simplify
Simplify…divide 2 and 8
3 examples – key is you can’t leave a radical in the denominator.
Introduce by asking what number can you multiply anything by and its identity doesn’t change. (1)

20. Example: Rationalizing the Denominator
Simplify denominator.
Break apart 504.
Take square root of y10 and write it outside the radical sign
Simplify
Multiply numerator and denominator by the denominator
Take square root of 36
3 examples – key is you can’t leave a radical in the denominator.
Simplify
Simplify
Simplify

21. Your Turn:
Simplify the expression.

22. Your Turn:
Simplify the expression. A. B. C.

23. Your Turn: Simplify the expression. Simplify denominator.
Simplify the numerator.
Multiply numerator and denominator by the denominator
3 examples – key is you can’t leave a radical in the denominator.
Simplify the terms outside the radical sign.
Simplify

24. Your Turn: Simplify the expression. Simplify denominator.
Simplify the numerator.
Multiply numerator and denominator by the denominator
3 examples – key is you can’t leave a radical in the denominator.
Simplify the terms outside the radical sign.
Simplify

25. Review: Simplifying Radicals
Steps
Requirements
No perfect square factors other than 1 are in the radicand.
No fractions are in the radicand.
No radicals appear in the denominator of a fraction.
Reduce the fraction, if possible.
Split the radical.
Square root perfect squares.
Look for perfect square factors and pull them out.
Rationalize the denominator, if needed.
Simplify if possible.

26. Assignment
10-2 Pt 2 Exercises Pg : #8 – 26 even