Lesson video

Hello there, I'm Mr. Lund.

And in today's lesson, we're going to be looking at dividing surds.

So when dividing surds, we follow a certain rule.

In general, the square root of a divided by the square root of b is equal to a divided by b, all square rooted.

Let me show you an example.

Here, the square root of 10 divided by the square root of five is equal to 10 divided by five, all square rooted.

That gives me an answer of the square root of two.

Let's try one more.

Let me show you.

The square root of 15 divided by the square root of three is equal to 15 divided by three, all square rooted.

That gives me an answer of the square root of five.

Pause the video here and restart when you have finished.

Here are the solutions to question number one.

How did you do? In the very last question, you should have ended up with an answer of three.

We always simplify surds when we can.

So when working with surds in general, we have to be mindful of certain things.

Don't forget to simplify if you possibly can.

Here, the square root of 12 divided by the square root of three gives you an answer of 12 divided by three, all square rooted.

That is the square root of four.

But don't forget to simplify your answers.

That gives us an answer of two.

Sometimes we have to manipulate surds.

In this example, I have two lots of the square root of three divided by the square root of two.

If I manipulate the first surds by expanding it, I end up with a surd which can be written as a square root of 12.

This looks a lot easier to deal with.

So 12 divided by two, all square rooted, gives you an answer of the square root of six.

Let's put what we've learned into practise.

Here are some questions for you to try.

Pause the video and restart when you're finished.

Here's the solutions question number two.

Hopefully, you're doing okay by now.

The very last question might have confused you slightly.

The same rules applies if you are dividing two numbers that are cube rooted.

So in this example, the cube root of 12 divided by the cube root of two finds you like cube root of six.

It's useful to recognise that division of two numbers can be written as a fraction.

Here, the square root of a divided by the square root of b is equal to square root of a over the square root of b.

That is also the same as saying a divided by b, all square rooted.

Let me show you an example.

Here, the square of four divided by the square root of two is equal to four divided by two, all square rooted, giving me an answer of the square root of two.

Have a look at this question.

What is the missing number? Hopefully, you found it.

It's a five.

The square root of 20 divided by the square root of four equals the square root of five.

Here's some questions for you to try.

Pause the video and restart when you're finished.

Here you go, the solutions to number three.

Notice question b, the square root of 12 can be written as two lots of the square root of three.

I must have got there myself.

Question d is another cube root question.

The cube root of 12 divided by the cube root of three finds you the cube root of four.

The cube root of four is not the same as the square root of four.

To end, Let's look at an example where we may apply our learning.

Here, We have a rectangle with an area of two lots of the square root of five centimetres squared, the width is the square root of two, and I want to work out what the missing length would be.

I can say that length is equal to area divided by width.

So the length is going to be two lots of the square root of five divided by the square root of two.

Manipulating the first surd will make this division much easier.

The square root of 20 divided by the square root of two finds me a length of the square root of 10.

Don't forget your units.

Here's a few quick examples for you to try.

Pause the video and restart when you have finished.

So here's the final two questions.

In the last question, you could have converted the integer three into square root of nine.

The area of the parallelogram could have been written as the square root of 54.

The square root of 54 divided by the square root of nine finds you the square root of six.

A little bit more complicated, but hopefully you did okay with that.