Geometric Perfect Square

like a perfect square?

25 is a perfect square, and so 25x 2 is a perfect square. It's the square of 5x.

Well we have one perfect square there, and we have another perfect square there.

It's a nice perfect square.

This is a perfect square.

4 is a perfect square.

49 is a perfect square.

45 is not a, 45 is not a perfect square. It's definitely not a perfect square.

49x squared is a perfect square.

49y squared is a perfect square.

Make these things a perfect square.

And 9 is a perfect square.

And 100 is a perfect square.

So this is a perfect square.

Well, now it's a perfect square.

Now let me write s to the fifth also as a product of a perfect square and a non perfect square. r to the fourth is obviously a perfect square.

Which allows us to break it down into a perfect square, and something that is not a perfect square.

Nothing else here is a perfect square.

This is looks like a perfect square, right?

And what do I mean by perfect square?

So we say, this is a perfect square.

So we do have a perfect square here.

Because 500 is not a perfect square, and x to the third is not a perfect square right from the get go.

And instead of just writing 20, let me write 20 as the product of a perfect square and a non perfect square.

If b squared minus 4ac is 16, we know that's a perfect square, you take the square root of a perfect square, we're going to have a rational answer.

You see, completing the square is all about making the quadratic equation into a perfect square, engineering it, adding and subtracting from both sides so it becomes a perfect square.

Right. Perfect! Predicated on plumb level, square and centered.

This is, let's see, this isn't a perfect square.

So this was a perfect square of a binomial.

This is actually, lucky for us, a perfect square.

Well we now know it is a perfect square.

And to complete the square, we just want to turn this into a perfect square.

left hand side into the perfect square of a binomial.

So essentially, he wants this to become a perfect square.

So maybe, just maybe this could be a perfect square.

So if it's a perfect square, I have two numbers.

When 4 is a perfect square, you might already recognize that.

9 is a perfect square root, so we can stop there.

It's taking every point and associating with it its perfect square.

So this it does fit the pattern of a perfect square.

Well, we see here, we have one perfect square right there.

Now this, hopefully you recognize this as already a perfect square.

We can only do this when this is a perfect square.

And luckily enough, this is a perfect square, so we can actually take the square root of it.