[MUSIC] We'll be learning about the square root property here.

Let's solve this equation for x. Now there are a few different ways to

solve this. First of all let's notice that the

left-hand side here, is the difference of 2 squares isn't it? Namely 3x quantity

squared minus 4^2. And remember in this case we have a

special formula for factoring the difference of 2 squares.

Namely A^2 - B^2 factors end to A - B * A + B.

So let's apply that here. With A = 3x and B = 4.

That is the left-hand side factors into 3x - 4 * 3x + 4.

And now we have a product of factors equal to 0 which means either the first

factor is 0 or the second factor is 0, which means that x = 4/3 or x is equal to

-4/3 which would be our answer. Now rather than solving this equation

this way, I could use the following property.

The square root property states that the solution to the equation C^2 = D where D

is a positive real number. RC = + or - the square root of D.

Now how could we use this here? Well, let's start by adding 16 to both sides of

this equation, which gives us 9x^2 = 16 and then dividing both sides by 9, we get

x^2 = 16 / 9. And by this property with C = x and D =

16 / 9, we get that the solutions to this equation.

Our x = + or - the square root of 16/9 or x = + or - 4/3.

Which are the same answers. Let's look at another example.

[SOUND] Let's solve this equation for y. Now here, [SOUND] it's much more

straightforward to just start off using our square root property.

With C = 2y - 5 and D = 9. Therefore the solutions to this equation

can be found as follows. We have C = + or - square root of D.

So C which in this case is 2y - 5 = + or - The square root of D which is 9, or 2y

- 5 = +/-3. Which means 2y - 5 is either equal to 3

or 2y - 5 = -3. And adding 5 to both sides we get 2y = 8

or 2y = 2. And now dividing both sides by 2 we get y

= 4 or y = 1 which would be our answer. And this is how we use this square root

property here. Thank you and we'll see you next time.