# Lesson video

In progress...

Hello my name's Miss Parnham.

In this lesson we will look at how surds of the form a root b can be written as root x.

This lesson naturally follows on from simplifying surds of the form a root b.

So it would be worthwhile working on that lesson before this one.

Writing numbers in surd form can make them difficult to quantify.

We have a vague idea of how big they are but when we need more accuracy it is more helpful to think of them as a single square root of a number.

Take this example.

I know root 6 is 2 point something.

But if I'm being asked is 3 root 6 more or less than 7 I need to think of it in a different way in order to answer that question.

So lets first rewrite 3 as root 9 and we can rewrite 7 as root 49 and then using the general rule of root a multiplied by root b is equal to root ab then root 9 root 6 is equivalent to root 54.

Now when we compare root 54 with root 49 we can straightaway see that root 54 is larger.

So 3 root 6 is greater or more than 7.

Here are some questions for you to try.

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

A good knowledge of the square numbers up to 225 and some quick mental multiplication will have made short work of these.

Here is another question for you to try.

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

This question was all about comparing with 10 or root 100 so for example 3 root 11 is equivalent to root 99 which is just below.

Whereas 5 root 5 is equivalent to root 125 which is even greater than root 121 or 11 so the real answer to that's between 11 and 12 so definitely above 10.

Here are some further questions for you to try.

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

Writing them in the form root x gives you root 60, root 72, root 90, root 125 and root 147 when they're ordered but please be careful to write your final answer as the original surds.

You can compare fractions with denominators written in surd form and use the same principles of finding equivalent surds that are single square roots of a number.

But in this case we must remember when comparing fractions with the same numerator but different denominators, the larger denominator will belong to the smaller fraction and vice versa.

Let's take a look at this question.

We can start by writing both denominators as a product of two surds and then converting to a single surd.

Here we see that root 54 is greater than root 48 but that means that 5 over root 54 is less than 5 over root 48.

So 5 over 3 root 6 is less than 5 over 4 root 3.

Here are some questions for you to try.

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