# Lesson video

In progress...

Hi, I'm Mr. Chan.

And in this lesson, we're going to learn how to add two surds, where you need to simplify.

Previously, we looked at adding like surds.

So in this example, root eight add root two.

It looks as though we cannot add them.

However, we can simplify root eight, into root four times root two, which further simplifies to two root two.

So once we think about root eight being simplified, we can rewrite root eight, as two root two add root two.

Now, we're in a position to add these two surds, we get a fine answer, three root two.

Here's a card match up activity for you to try.

Pause the video to complete the task.

Restart the video, once you're finished.

This question was asking you to just practise simplifying some surds, simplifying root eight was covered in the example.

So hope you got that right.

Root eight simplifies to two root two.

Root 50, we can think of that as root 25 times two, root 25 simplifies to five, so we get the answer, five root two.

Root 24, we can think of that as root four times root six, that gives you the answer, two root six.

For the question four root 27, simplifying that we would look at simplify the root 27, which we can simplify, to think of that as root nine, root three, route nine simplifies to three.

So we get four times three, root three, we get the answer, 12 root three.

And the final number card, two root 12, simplifies to four root three.

Hopefully you got all those correct.

So now you've had some practise simplifying surds.

Let's have a look at another example.

Where on the surface, it looks like we cannot add these surds, because they are not alike.

But we might have to think about simplifying one of the surds, or maybe both, in order to add them.

So we have the question root 48, add five root three.

Let's think about simplifying the root 48.

Simplifying that becomes root 16 times three, which further simplifies to four root three.

So the question now becomes, four root three, add five root three.

To give a final answer, nine root three.

Here's some questions for you to try.

Pause the video to complete the task.

Restart the video, once you're finished.

Here are the answers for question two.

In part A, root eight add three root two.

You're going to have to simplify root eight for this part of the question, roots eight simplifies to two root two.

So, adding those two sides together, will give you an answer, five root two.

In part B, two root three add five root 12.

In this part of the question, you're going to have to simplify the five root 12, that simplifies to 10 root three, adding two root three, add 10 root three, will give you the answer, 12 root three.

In part C, simplifying five root 27 in this question, will give you an answer, 17 root three.

In part D, this one's starts with different, because you have to simplify both of those surds, in order to add them, six root eight will simplify to 12 root two, add root 50, will simplify to five root two, adding those two together, will give you a fine answer, 17 root two.

In part E, root 63 simplifies to three root seven, adding that to two root 28 which simplifies to four root seven, gives you an answer, seven root seven.

In part F, six root 27 simplifies to 18 root three, add two root 75 simplifies to 10 root three, 18 root three, adding 10 root three, gives you a final answer, 28 root three.

Hopefully you did really well on those.

In this example, whereas to work out the perimeter, of this isosceles triangle.

A reminder that the perimeter, is worked out by calculating the distance around the outside of a ship.

So, in order to work out the perimeter, I'm going to take each side length, and add them together.

Now, we can see that these surds are not alike, so, initially we're thinking that we can't add this.

However, we can simplify these surds as follows.

Root 28 will simplify to root four, root seven, similarly with the other root 28, into root four root seven, and on further simplification, these root four root seven, will simplify to two route seven.

So the calculation for the perimeter becomes, two root seven, add two root seven, add root seven.

Add a total to the perimeter gives us a final answer, five root seven centimetres.

Here's some questions for you to try.

Pose the video to complete the task.

Restart the video, once you're finished.

In this question you're asked to find the perimeter of firstly a triangle, and then a rectangle.

So for the triangle, we're going to have to find the perimeter, by adding all the sides together.

Now all of those certainly simplifying, before we can do that.

So, when we simplify these sets in the question, four root 27, will simplify two 12 root three, root 12 will simplify to two root three, and route 48 will simplify to four root three.

So adding these three surds together, 12 root three, add two root three, add four root three.

It gives a final answer for the perimeter of this triangle, to 18 root three centimetres.

For the rectangle, remember the opposite sides are equal in length, so we have to simplify the surds in order to find the perimeter, root 32 simplifies to four root two, and root eight simplifies to two root two, adding all the four sides together, gives us the answer, 12 root two centimetres.

Here's a question for you to try.

Pose the video to complete your task, restart the video, once you're finished.

Here's the answer for this question.

You can see next to each number card, I've simplified the surd inside.

And once I've done that, it's just a simple case of choosing three number cards, which will give me a total, of nine root five.

So in this case, I've chosen the number of cards root 20, root 45 and root 80.

Adding those three surds together once they're simplified, will give me a total, of nine root five.

Hopefully you got that correct answer.

That's all for this lesson.

Thanks for watching.