1 6 Objectives The student will be able
1. 6 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
If x 2 = 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. Find the square root: 11, -11 4. Find the square root: 21 5. Find the square root:
6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth. 6. 82, -6. 82
LEAVE IN RADICAL FORM Perfect Square Factor * Other Factor = = = = =
1. Simplify Find a perfect square that goes into 147.
2. Simplify Find a perfect square that goes into 605.
Simplify 1. 2. 3. 4. . .
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, . . .
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.
4. Simplify Find a perfect square that goes into 49. 5. Simplify
Simplify 1. 2. 3. 4. 3 x 6 3 x 18 6 9 x 18 9 x
6. Simplify Multiply the radicals.
7. Simplify Multiply the coefficients and radicals.
Simplify 1. 2. 3. 4. . .
How do you know when a radical problem is done? 1. No radicals can be simplified. Example: 2. There are no fractions in the radical. Example: 3. There are no radicals in the denominator. Example:
8. Simplify. Divide the radicals. Whew! It simplified! Uh oh… There is a radical in the denominator!
9. Simplify Uh oh… Another radical in the denominator! Whew! It simplified again! I hope they all are like this!
10. Simplify Uh oh… There is a fraction in the radical! 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!
- Slides: 20