What are the characteristics of a radical equation?
how is solving radical equations similar to solving linear equations?
why is it important to check the solutions to a radical equation?
create your own radical equation. describe in complete sentences and demonstrate the process in finding its solution(s)

What are the characteristics of a radical equation?

Radical equations are those equations where the variable is inside a radical.
For example: √x - 5 = 0 is a radical equation but x -√5 = 0 is not a radical equations.

How is solving radical equations similar to solving linear equations?

You search to isolate the variable, by performing identical operations on both sides of the equation.

Why is it important to check the solutions to a radical equation?

This is important when the index of the root is an even number. For example 2. When you square a square root you force the results to be positive and this may hide the real condition of the original equation.

For example, √x + 5 = 0

=> √x = -5

=>(√x)^2 = (-5)^2

=> x = 25

When you check: √x + 5 =√25 + 5 = 5 + 5 = 10 which is contradictory with the original equation. You have to discard the solution, becasue none real number exists whose square root is negative, which means that √x + 5 = 0 does not have a real solution.

Create your own radical equation. Describe in complete sentences and demonstrate the process in finding its solution(s)

√(3x+1) - 10 = 0

1) isolate the radical: √(3x + 1) = 10

2) Square both sides: [√(3x + 1)]^2 = 10^2

=> 3x + 1 = 100
=> 3x  = 99
=> x = 33

3) Check

√[(3(33) + 1] - 10 = √(99 + 1) - 10 = √100 - 10 = 10 - 10 = 0

Then the solution is correct

Answer for 2: his profit would be $2.88 explanation: you have to first multiply 72 and 0.12 together to get $8.64 once you do that you know how much money the shopkeeper made from selling the candy bars individually. so you have to do 8.64-5.76=2.88 hope that ; )answer for 3: yeah i’m sorry i have no idea what number 3 is. i’m sorry i couldn’t with that.