All Algebra II Resources
Example Questions
Example Question #1 : Solving Radical Equations
Solve for :
None of the other responses is correct.
None of the other responses is correct.
One way to solve this equation is to substitute for and, subsequently, for :
Solve the resulting quadratic equation by factoring the expression:
Set each linear binomial to sero and solve:
or
Substitute back:
- this is not possible.
- this is the only solution.
None of the responses state that is the only solution.
Example Question #2 : Solving Radical Equations
Solve the following radical equation.
We can simplify the fraction:
Plugging this into the equation leaves us with:
Note: Because they are like terms, we can add them.
Example Question #3 : Solving Radical Equations
Solve the following radical equation.
In order to solve this equation, we need to know that
How? Because of these two facts:
- Power rule of exponents: when we raise a power to a power, we need to mulitply the exponents:
With this in mind, we can solve the equation:
In order to eliminate the radical, we have to square it. What we do on one side, we must do on the other.
Example Question #4 : Solving Radical Equations
Solve the following radical equation.
In order to solve this equation, we need to know that
Note: This is due to the power rule of exponents.
With this in mind, we can solve the equation:
In order to get rid of the radical we square it. Remember what we do on one side, we must do on the other.
Example Question #5 : Solving Radical Equations
Solve for x:
To solve, perform inverse opperations, keeping in mind order of opperations:
first, square both sides
subtract 1
divide by 2
Example Question #6 : Solving Radical Equations
Solve for x:
To solve, perform inverse opperations, keeping in mind order of opperations:
take the square root of both sides
subtract 19 from both sides
square both sides
Example Question #7 : Solving Radical Equations
Solve for x:
To solve, use inverse opperations keeping in mind order of opperations:
divide both sides by 5
square both sides
add 12 to both sides
Example Question #8 : Solving Radical Equations
Solve for .
To get rid of the radical, we square both sides.
Example Question #9 : Solving Radical Equations
Solve for .
No answer
No answer
To get rid of the radical, we need to square both sides. The issue is radicals don't generate negative numbers unless we talk about imaginary numbers. In this case, our answer choice should be no answer.
Example Question #10 : Solving Radical Equations
Solve for .
Square both sides to get rid of the radical.
Subtract on both sides.
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