1. Objectives The student will be able to:
1. simplify square roots, and
2. simplify radical expressions.
SOL: A.3
Designed by Skip Tyler, Varina High School

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. Find a perfect square that goes into 147.
1. Simplify
Find a perfect square that goes into 147.

7. Find a perfect square that goes into 605.
2. Simplify
Find a perfect square that goes into 605.

8. Simplify .

9. 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.

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

11. Simplify
3x6
3x18
9x6
9x18

12. 6. Simplify
Multiply the radicals.

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

14. Simplify .

15. How do you know when a radical problem is done?
No radicals can be simplified. Example:
There are no fractions in the radical. Example:
There are no radicals in the denominator. Example:

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

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

18. 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!