1. Aim: How do we solve radical equations?
Do Now: Describe the steps for solving:
x2 – 80 = 0
x2 = 80
add 80 to both sides
take square root of both sides
simplify
Describe the reverse process
square both sides
x2 = 80
x2 – 80 = 0
subtract 80 from both sides
How do we solve?
solve by first squaring
both sides.

2. Perfect Squares 12
144 11
121
100 10 9 81 8 64 7 49 6 36 5 25 4 16 3 9 4 2 1

3. Simplifying Radicals
KEY: Find 2 factors for the radicand - one of which is the largest perfect square possible
Multiplying Radicals

4. Dividing Radicals
If quotient is not a perfect square
you must simplify the radicand.

5. Adding/Subtracting Radicals
Must have same radicand and index
Add or subtract coefficients and combine result with the common radical
Coefficient
Common Radical
Combined Result
Unlike radicals must first be simplified
to obtain like radicals
(same radicand-same index), if possible.
ex.

6. Solving Radical Equations
Solve and check:
Isolate the radical:
(already done)
Square each side:
Solve the derived
equation:
x2 – 9x + 16 = 0
use quadratic
formula:

7. Solving Radical Equations
Solve and check:
Isolate the radical:
(already done)
Square each side:
Solve the derived
equation:
x – 2 = 25
x = 27
Check:
(x – 2)1/2 = 5
[(x – 2)1/2]2 = 52
alternate:
5 = 5

8. ? Extraneous Roots Solve and check: Isolate the radical:
Square each side:
Solve the derived
equation:
2y – 1 = 9
2y = 10
y = 5
Check:
y = 5 is an extraneous root;
there is no solution! ?
3 + 7 = 4

9. Solving Radical Equations
Solve and check:
Isolate the radical:
Square each side:
Solve the derived
equation:
x2 – 2x + 1 = x + 5
x2 – 3x – 4 = 0
(x – 4)(x + 1) = 0
x = x = -1
Check
each
root: ?
4 = 4
x = -1 is an extraneous root

10. Solving Radical Equations
Solve and check: ?
Square each side:
Solve the derived
equation:
32(x – 2) = 22(x + 8)
9(x – 2) = 4(x + 8)
9x – 18 = 4x + 32
x = 10
x = 10 checks out as the solution

11. Model Problem
The radical function is an
approximation of the height in meters of
a female giraffe using her weight x in
kilograms. Find the heights of female giraffes
with weights of 500 kg. and 545 kg.
Evaluate for 500:
Evaluate for 545:
 3.17 m.
 3.27m.

12. Model Problem
The equation gives the time T in seconds it takes a body with mass 0.5 kg to complete one orbit of radius r meters. The force F in newtons pulls the body toward the center of the orbit.
a. It takes 2 s for an object to make one revolution with a force of 10 N (newtons). Find the radius of the orbit.
b. Find the radius of the orbit if the force is 160 N and T = 2. a.