1. Lesson 9.2 Simplifying Square Roots
Essential Question: How do you simplify a radical expression?

2. Before we start…
9 =? 25 =? 9∙25=? 225 =? 3∙5=? What do you notice?

3. What is a square root?
A number r is a square root of a number s if r2 = s.
A positive number s has two square roots.

4. What is a radical? What is a radicand?
A radical is the expression
A radicand is the number s beneath the radical sign

5. What is simplest form of a radical expression?
A square root expression is simplified if:
No radicand has a perfect-square factor other than 1
No fractions are in the radicand
There is no radical in a denominator

6. Simplifying Square Roots
You can use the properties of square roots to simplify expressions containing square roots.
The Product Property
The Quotient Property
Rationalizing the Denominator

7. How do you simplify radical expressions?
Factor out perfect square factors.
Take the square root of the perfect square factor(s).
Simplify.

8. What is the Product Property of Radicals?
The square root of a product equals the product of the square roots of the factors. 𝑎𝑏 = 𝑎 𝑏

9. What is the Quotient Property of Radicals?
The square root of a quotient equals the quotient of the square roots of the numerator and denominator. 𝑎 𝑏 = 𝑎 𝑏

10. Simplify 80
180

11. Simplify 20 48

12. Simplify 27 24

13. Simplify
6 ∙ 21
3 ∙ 15

14. Simplify
10 ∙ 15
8 ∙ 28

15. Simplify
4 81
9 64

16. Simplify
11 25
7 16

17. Simplify
24 𝑠 2
54 𝑡 2

18. Simplify
75 𝑟 2
56 𝑚 2

19. Simplify
32 𝑛 2
40 𝑥 2

20. Simplify
16𝑧 49
32 𝑦 2 81

21. Accident Investigation After a car accident, a police officer measures the length l (in feet) of a car’s skid marks. The expression 27𝑙 gives the car’s speed in miles per hour at the time the brakes were applied.
Write the expression in simplest form.
The skid marks are 125 feet long. Use the simplified expression to approximate the car’s speed when the brakes were applied.

22. Boat Travel The expression 16𝑥 9 gives the maximum speed (in nautical miles per hour) that certain boats can travel, where x is the boat’s water line length in feet.
Write the expression in simplest form.
A boat’s water line length is 30 feet. Use the simplified expression to approximate the boat’s maximum speed.

23. Falling Object The expression ℎ 16 gives the time (in seconds) it takes an object to fall h feet.
Write the expression in simplest form.
Find the length of time it takes for an object to fall 120 feet. Give your answer to the nearest tenth of a second.

24. How do you simplify a radical expression?

25. Ticket Out the Door
Simplify 63