Lesson video

Hello everyone.

Today we're going to be learning about rationalising surds.

Hello everyone.

Let's have a quick recap of equivalent fractions.

If I have a fraction, and multiply the numerator and the denominator of that fraction, by the same number.

In this case, I multiply the numerator by three and the denominator by three, I end up with an equivalent fraction.

It looks slightly different, but the value of a over b, and 3a over 3b, is the same.

Now, if a fraction has a surd in the denominator, we can manipulate the fraction, and remove the surd by finding an equivalent fraction.

This is called rationalising.

I'm going to multiply the numerator and the denominator by the denominator of the original fraction.

You see that.

Now, if I'm multiplying b times by the square root of a, I end up with b times by the square root of a, which looks like that.

And if I multiply, the square root of a by the square root of a, I just end up with, a.

That is called rationalising, of the denominator.

So, this fraction is being rationalised.

True or false? This is false, it has not been rationalised.

I haven't multiplied, by the denominator of the original fraction.

So I end up with a surd in the denominator of the answer.

It is an equivalent fraction, but it has not been rationalised.

Let me show you an example, rationalise, the fraction two over the square root of three.

I do this by multiplying the numerator, and the denominator by the denominator of the original fraction.

If I multiply the square root of three by the square root of three, I find a rational number of three.

If I multiply two by the square root of three, I end up with a new numerator, of two lots of the square root of three.

I have rationalised my original fraction.

Okay.

Let me show you a second example.

Here we go.

This comes up in your exam, you're asked to rationalise five over the squared to two.

What do you have to do, First of all, multiply the numerator and the denominator by the denominator of the original fraction.

The square root of two multiplied by the square root two just gives you two, and then five times the square root to two gives you that.

Now I see it.

Okay.

Okay.

So here's some examples for you to have a look at.

Pause the video and return when you have finished.

Here are the solutions to question number one.

In the final question, question e, you can simplify your answer.

10 over six as a fraction, simplifies to five over three.

If you have a surd in the numerator, just leave the surd there.

So, quick question.

What is the missing number? That's right, it's five.

Quick fire.

What is the missing value? Hopefully, you recognised it as a six.

So, pause the video here and have a go the next three slides of questions.

And don't forget to simplify if you cannot, return when you've finished.

See you in a bit Here are the solutions to question number two.

Again, question e, can be simplified.

Here are the solutions to question number three.

Here are the solutions to question number four.

When you have co-efficiency influence of surds there are a few different ways you can deal with it, but, you can expand the search.

So for example, two lots of the square root two could be written as the square root of eight, and work with them like that.

Or in this case, question number five, where it says, eight over two as the co-efficients, you can simplify that down, so you've just got four the square root of three divided by the square root two.

So, a few different ways to work with those, practises needed.