## 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.