1. 11-1 Simplifying Radicals

2. If x2 = y then x is a square root of y.
In the expression , is the radical sign and 64 is the radicand.
1. Find the square root: 8
2. Find the square root:
-0.2

3. 3. Find the square root: 11, -11 4. Find the square root: 21

4. 6. Use a calculator to find each square root
6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth.
6.82, -6.82

5. What numbers are perfect squares?
1 • 1 = 1
2 • 2 = 4
3 • 3 = 9
4 • 4 = 16
5 • 5 = 25
6 • 6 = 36
49, 64, 81, 100, 121, 144, ...

6. Multiplication property of square roots
Properties of Radicals
Multiplication property of square roots
Division property of square roots

7. Properties of Radicals
What does this really mean?
which we all know equals 10
it can be rewritten as: or
which we all know equals 10

8. How can I use this?
To write a radical in simplest form you must make sure:
The radicand has no perfect square factors
The radicand has no fractions
The denominator of a fraction has no radical
This property addresses the first point

9. Find a perfect square that goes into 75.
To simplify
Find a perfect square that goes into 75.

10. Find a perfect square that goes into 600.
2. Simplify
Find a perfect square that goes into 600.

11. Simplify .

12. How do you simplify variables in the radical?
Look at these examples and try to find the pattern…
What is the answer to ?
As a general rule, divide the exponent by two. The remainder stays in the radical.

13. Find a perfect square that goes into 49.
4. Simplify
Find a perfect square that goes into 49.
5. Simplify

14. Simplify
3x6
3x18
9x6
9x18

15. 6. Simplify
Multiply the radicals.

16. Multiply the coefficients and radicals.
7. Simplify
Multiply the coefficients and radicals.

17. Simplify .

18. How do you know when a radical problem is done?
No radicals can be simplified. Example: not done because 4 is a factor
There are no fractions in the radical. Example: not done because it is a fraction
There are no radicals in the denominator. Example: not done because radical 5 is in
denominator
Division property of square roots helps with points 2 and 3

19. There is a radical in the denominator!
8. Simplify.
Divide the radicals.
Uh oh…
There is a radical in the denominator!
Whew! It simplified!

20. 9. Simplify Uh oh… Another radical in the denominator!
Uh oh…
Another radical in the denominator!
Whew! It simplified again! I hope they all are like this!

21. 10. Simplify Since the fraction doesn’t reduce, split the radical up.
Uh oh…
There is a fraction in the radical!
10. Simplify
Since the fraction doesn’t reduce, split the radical up.
How do I get rid of the radical in the denominator?
Multiply by the “fancy one” to make the denominator a perfect square!