Part 1
In this video, we are going to look at solving equations by taking the square root.
For example:
If we are given the equation
we can solve for x by taking the square root of both sides.
This will leave us with just x. However, the square root of 9 isn’t just 3. It can be positive or negative 3. So
If we had something more complicated like
then we would first have to get the by itself. So, first add 5 to both sides to isolate the . Now we are left with . Then take the square root of both sides
Part 2
In this video, we are going to look at solving equations by taking the square root more in depth.
For example:
If we are given the equation
we can first take the square root of both sides.
This will leave us with
Then subtract 5 from both sides and get
and
This leads us to a final answer of
If we had something more complicated like
then we would first have to get the by itself. So, first add 3 to both sides to isolate the . Now we are left with . Then take the square root of both sides
Subtract 2 from both sides
and
So
Examples of Solving An Equation By Taking The Square Root
Example 1
What are the solutions to ?
Solve for by taking the square root of both sides.
We can write break this down into:
The final answer is
Our solutions are:
and
Example 2
What are the solutions to ?
First, let’s subtract to both sides
Next, solve for by taking the square root of both sides.
So we have two answers:
and
Video-Lesson Transcript – Part 1
Let’s go over solving equations by taking square roots.
If we have this equation:
To solve for the value of , we have to get the square root.
The tricky part here is the square root of .
Because it’s not just positive, it can also be negative.
So we have two answers:
and
Let’s have a more complicated one.
In order to solve this, we have to leave by itself first.
So let’s get rid of by adding on both sides of the equation.
So our solutions are
{}
It’s also possible that we get one that doesn’t work out.
So we’ll leave it at that.
Our final answers are
and
Let’s have another one
We can write break this down into:
I chose to write this because square root of is possible.
So our answer is
Our solutions are:
and
Video-Lesson Transcript – Part 2
Let’s take a more in depth look at solving quadratic equations by taking square root.
Just to recap:
If we have , to solve this
So our solution set is
{}
We could use the same method if we have
Rather than multiplying, let’s just get the square roots of both sides.
Now, let’s get the value of
So we have two answers:
and
Our solution set is
{}
Let’s look at this one
Let’s do the same thing
So we have
and
Our solution set is
{}
Let’s have a different equation such as
To solve this, we have to get rid of first.
So we have two answers:
and
Our solution set is
{}
Let’s see this one
Let’s see what happens when we solve this
Since we can not get the square root of , we’ll leave it as:
Then isolate
This can already be our answers.
{}
After you finish this lesson, view all of our Algebra 1 lessons and practice problems.