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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 #1 : 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 #2 : 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 #3 : Solving Radical Equations
Solve for :
or
no solution
or
or
or
To solve, first square both sides:
squaring the left side just givs x - 3. To square the left side, use the distributite property and multiply :
This is a quadratic, we just need to combine like terms and get it equal to 0
now we can solve using the quadratic formula:
This gives us 2 potential answers:
and
Example Question #9 : Solving Radical Equations
Solve for :
or
or
or
If we consider a quadratic equation one where , this is a quadratic with . We can re-write it so that it is set equal to 0, and then we can use the quadratic formula or a different method to solve:
or in terms of ,
Putting this into the quadratic formula, we get
This gives us 2 answers, and
Remembering that these are potential answers for u, we can finish solving:
square both sides
and
square both sides
Example Question #10 : Solving Radical Equations
Solve for .
To get rid of the radical, we square both sides.
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