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Hello, my name is Ms.Parnham.

In this lesson we're going to learn how to simplify surd to the form A root B.

Hopefully you have already completed the lesson on simplifying a simple surd as today's lesson builds on that knowledge.

We learned that the root of a number can be expressed as the product of the square root of its factor pairs.

And we look for a factor pair that contains the largest square number possible.

So looking at root 20, the largest square number which is a factor of 20 is four.

So we re-write root 20 as root four, root five and then that simplifies to two root five.

So it stands to reason that two root 20 is going to be twice as big as two root five, namely, four root five.

And using the same logic, seven root 20 will be seven times bigger than two root five, 14 root five.

Here are some questions for you to try, pause the video to complete the task and restart the video when you're finished.

Here are the answers, hopefully you saw the patterns when we increase the number in front of root eight or root 27 each time.

Here are some more questions for you to try.

Pause the video to complete the task and then restart the video when you're finished.

Here are the answers, keeping in mind that root eight is two root two and root 27 is three root three makes it relatively easy to find multiples of them.

Sometimes surd of the form A root B aren't written as simply as possible.

In this case, the greatest square number factor of 24 is four.

So we re-write root 24 as root four, root six.

Then we make root four into two and three multiplied by two is six.

So the correct simplification of three root 24 is six root six.

And we can use this when we're simplifying fractions.

So here we have three root 24, which we already know is six root six.

We can use the same sort of process with two root 45.

Root 45 can be thought of as root nine, root five and root nine is three and two multiply by three is six.

So here we have a fraction that can be simplified by cancelling common factors.

We can cancel the six from both the numerator and the denominator.

So three root 24 over two root 45 simplifies to root six over root five.

We can you use the same sort of principle when we're simplifying ratio.

Here, we already know that three root 24, is six root six.

We can use the same process with five root 18 which simplifies to 15 root 2.

But here we have a common factor of three, so that gives us two root six to five root two.

But we're not quite finished because look at the surds, root six and root two, both have a common factor of root two, so we can divide it by root two.

That gives us two root three to five and that's a simplified ratio.

Here are some questions for you to try.

Pause the video to complete the task and restart the video when you're finished.

Here are the answers, good knowledge of square numbers is so useful.

Take part eight for example, you might re-write root 200 as root 25 root eight or five root eight.

But earlier in this lesson, we saw that, that was actually simplified further to 10 root two, which is multiplied by seven to get the final answer of 70 root two.

That's fine to simplify using multiple steps.

Here are some further questions for you to try.

Pause the video to complete the task and restart the video when you're finished.

Here are the answers, Teddy made the mistake we discussed earlier of not identifying the greatest square number factor of 48.

Nevertheless, he could improve the answer he's given by re-writing root 12 as root four, root three or two root three.

And then when he multiplies that by 20, he will give the simplest solution of 40 root three.

That's all for this lesson, thanks for watching.