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Hello everyone.

Today's lesson is on dividing surds With coefficients.

When dividing surds, we must follow this routine.

The square root of a, divided by the square root of b is equal to a over b, all square rooted.

Sometimes we see surds with numbers in front.

These numbers are called coefficients.

When dividing surd with numbers in front of them, we need to follow a slightly different rule.

Here, the square root of a, has a coefficient of C and I'm going to divide it by another surd.

This surd also has a coefficient.

If I were to divide both, I divide the coefficients first and then divide the surd and combine that in one expression.

Okay.

Let me show you an example.

Here I have two surds, both with coefficients that I would like to divide.

The first set has a coefficient four, the second surd has a coefficient of two.

So I'm going to go ahead and I'm going to divide those two numbers.

Then I'm going to divide each of the surds.

So 10 divided by five, all squared rooted.

Let's simplify that expression and there we go, two the square root of two.

Two lots of the square root two.

Okay, wonderful.

Let's show you another example.

Here we have six lots of the square root 10, I'm going to divide it by two lots of the square root five.

Let's go ahead and divide those coefficients.

Six divided by two, let's divide those surds, 10 divided by five, all square rooted and then simplify our expression and give us three the square root of two.

So three lots of the square root of two.

Here are some questions for you to try.

Pause the video and restart when you're finished.

So here are the solutions to question number one, and it looks like there's only one false statement there, which is d, two lots of square root of five, divided by the square root of five, just leaves you with the answer of two.

Here's a question for you to have a think about.

Is this true or false? It's true.

The square root of six divided by square root three can be shown as a fraction, square root of six over the square root three.

Let's move on and look at examples.

Here's some examples with coefficients.

Is this true or false? It's true.

Okay.

So we can display division as a fraction.

Here are some questions for you to try.

Pause the video and restart when you're finished.

Okay.

Welcome back.

Here's the answers to question number two, it looks like hopefully you'll be rolling along with these types of questions now, it looks like e is the most interesting question there because we have surd displayed as a fraction.

So that's 16 lots of the square root six, divided by two lots of square root of three and then we're going to divide once more and that should give you an answer of eight altogether.

So it's a bit like saying, 16 lots of square root six, divided by two lots of square three and then again, divided by the square root of two.

Okay.

A little quick question then.

What are the missing numbers? There we go.

Did you get that 15 as a coefficient, and five inside the square root there.

So once again, pause the video, have a go at these questions.

There are two sets of slides of this slide, and then another one after.

See you in a while.

Here's the answers for question three and four.

You can display three times the square root of six as the square roots 54.

If it's acceptable, it's nice to kind of simplify, in its expanded format.

Sorry.

in it's factorised form of three lots of the square root of six and then question four, a and b kind of get you thinking about where the numbers should be, but hopefully you're sort of, you're getting your way through those.

Yeah.

And finally questions, five and six, we have some area problems and we're given the area of a rectangle in question five, and we're going to divide it by the width, which is a 10 lots of square root two, ultimately that would give us an answer of four.

So you should have found square root of 16, which simplified gives you an answer of four.

And then the last one is a parallelogram, pretty much the same principle, as long as you are using the perpendicular height.

So are you using the perpendicular height? Yeah.

That's good if you are.

So we've got nine lots of square root of six.

You could expand that if you wanted it to see it in a different form.

What is that nine times? What is that? 81 times by six.

I mean, that's a square root of 486 and then we were dividing that by, so nine times by six, divided that by 54 and that should have given you an answer of the square root of nine, which of course is three.

So a bit more complicated.

I have to get the old calculator out for that one.

Okay.