Radical Functions - Pre-Calculus
Card 0 of 9
Solve for 
Solve for
In order to solve this equation, we need to isolate the radical. In order to do so, we subtract 3 from both sides which leaves us with:
To get rid of the radical, we square both sides:
the radical is then canceled out leaving us with 
We solve for 
by dividing by 4:
In order to solve this equation, we need to isolate the radical. In order to do so, we subtract 3 from both sides which leaves us with:
To get rid of the radical, we square both sides:
the radical is then canceled out leaving us with
We solve for
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Solve for 
Solve for
In order to get rid of the radical, we square both sides:
Since the radical cancels out, we're left with 
Subtracting both sides by 1 gives us 
We then divide both sides by 6 to get 
.
In order to get rid of the radical, we square both sides:
Since the radical cancels out, we're left with
Subtracting both sides by 1 gives us
We then divide both sides by 6 to get
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Solve:
Solve:
- To remove the radicals, raise both sides of the equation to the second power:
- To remove the radical, raise both side of the equation to the second power:
- Now simplify, write as a quadratic equation, and solve:
- Checking for extraneous solutions.
Plugging in 
Plugging in 
Since the square root of negative 5.4 gives us an imaginary solution we conclude that the only real solution is x=3.
- To remove the radicals, raise both sides of the equation to the second power:
- To remove the radical, raise both side of the equation to the second power:
- Now simplify, write as a quadratic equation, and solve:
- Checking for extraneous solutions.
Plugging in
Plugging in
Since the square root of negative 5.4 gives us an imaginary solution we conclude that the only real solution is x=3.
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Which of the following is a solution to the following equation?
Which of the following is a solution to the following equation?
We begin by sqaring both sides of the equation. On the left side, the square root simply disappears, while on the right side we square the term.
We then set the left side equal to 0 by subtracting everything on that side.
We then factor
Therefore, 
With problems of this type, it is always wise to double check for any extraneous roots (answers that don't actually work for some reason). However, in this case both answers work. Since
is the only option among our choices, we should go with it.
We begin by sqaring both sides of the equation. On the left side, the square root simply disappears, while on the right side we square the term.
We then set the left side equal to 0 by subtracting everything on that side.
We then factor
Therefore,
With problems of this type, it is always wise to double check for any extraneous roots (answers that don't actually work for some reason). However, in this case both answers work. Since
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Solve for 
and use the solution to show where the radical functions intersect:
Solve for
To solve, first square both sides of the equation to reverse the square-rooting of the binomials, then simplify:
Now solve for 
:
The x-coordinate for the intersection point is 
.
Choose one of the two radical functions that compose the equation, and set the function equal to y. The more simple a function is, the easier it is to use:
Now substitute 
into the function.
The y-coordinate of the intersection point is 
.
The intersection point of the two radical functions is 
.
Now graph the two radical functions:
, 
To solve, first square both sides of the equation to reverse the square-rooting of the binomials, then simplify:
Now solve for
The x-coordinate for the intersection point is
Choose one of the two radical functions that compose the equation, and set the function equal to y. The more simple a function is, the easier it is to use:
Now substitute
The y-coordinate of the intersection point is
The intersection point of the two radical functions is
Now graph the two radical functions:
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Which of the following is and accurate graph of 
?
Which of the following is and accurate graph of
Remember 
, for 
.
Step 1, realize where 
starts: A) observe 
never occurs, B) zero-out the radical component of 
;
C) The resulting point is 
.
Step 2, find simple points for 
after 
:
, so use 
;
The next resulting point; 
.
, so use 
;
The next resulting point; 
.
Step 3, draw a curve through the considered points.
Remember
Step 1, realize where
C) The resulting point is
Step 2, find simple points for
The next resulting point;
The next resulting point;
Step 3, draw a curve through the considered points.
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Solve the following radical equation.
Solve the following radical equation.
When dealing with a radical equation, do the inverse operation to isolate the variable. In this case, the inverse operation of a square root is to square the expression. Thus we square both sides to continue. This yields the following.
When dealing with a radical equation, do the inverse operation to isolate the variable. In this case, the inverse operation of a square root is to square the expression. Thus we square both sides to continue. This yields the following.
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Solve the rational equation: 
Solve the rational equation:
Square both sides to eliminate all radicals:
Multiply both sides by 2:
Combine and isolate x:
Square both sides to eliminate all radicals:
Multiply both sides by 2:
Combine and isolate x:
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Solve this radical function:
Solve this radical function:
Add x to both sides:
Square both sides:
Simplify:
Factor and set equal to zero:
Add x to both sides:
Square both sides:
Simplify:
Factor and set equal to zero:
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