Which answer is correct if 9√2 is rewritten in the form √x?

Is the following statement true or false?

Which 2 integers does 5√6 lie between?

Write a√b in form √x

﻿I'm Mr Chan. In this lesson we're going to learn how to adds two surds. Following our book's example, let's have a look at what like surds are. Like surds are surds that have the same number inside the root symbol, and you can have multiples of those. So let's have a look at some. Here we have several surds. Some are like and some are not like. Can you spot which ones are the like ones? As you can see, we've grouped all the like ones together, and the ones that are not like in the other part of the table. The ones that are like all contain the number five in the surd symbol. So let's have a look at some examples of adding two surds. In question one, root 3 add 2 root 3. Well those two surds are like, so we can actually add those together. We've got 1 of root 3, adding 2 to root 3, altogether we would have 3 lots of root 3, so that would be our answer. In question two, root 5, add 2 root 3. But those two surds are not like, so we cannot actually add those together, so we would just leave our answer as root 5 add 2 root 3. We can't add those. In questions three, 2 root 7, add 6 root 7. Those two surds are like, we can actually add those together, we would get in total 8 root 7 as our final answer. In question four, root 4 add 5 root 2. Well clearly those two surds are not like, however, root 4 does have an answer that we can simplify a little bit further, and we should know that root 4, the square of root 4, is just simply 2. So we can simplify root 4 into 2 which we should do. And we cannot add that to 5 root 2 because those are not like, that would be our final answer. 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. In part A, root 5 and root 7 are not like surds, so we can't add those. In part B, root 5 and root 5, they are like surds, so we can add those together to give an answer 2 root 5. In part C, we should know that root 9 equals 3, but when we try and add 3 to root 3, we cannot simplify those because they're not like, and we wouldn't get the answer 3 root 3, so that statement's false. In part D, we again have like surds that we can add together, similarly with part E, those root 7s are all like, so we can add those together, to give a final answer 10 root 7. The correct answers for those statements that are false are given there. Here's another question for you to try. Pause the video to have a go, and restart the video when you're finished. Here are the answers for question two. All of these questions contain like surds, so hopefully you found these pretty straightforward to add together. In this example, we're asked to find the perimeter of the parallelogram. A reminder that the perimeter is the distance around an object, so we'd have to add all these side lengths together. So in order to find the perimeter, we're going to add 5 root 3, add onto that 2 root 3, add 5 root 3, and finally add the final side length 2 root 3. These are all like surds, which we can add together to give a total of 14 root 3, and as our final answer that would be our perimeter for this parallelogram, 14 root 3cm. Here are two questions for you to try. Pause the video to complete the task, and restart the video when you're finished. Here are the answers for question three, where you're asked to find the perimeter of each shape. Part A, this is a rectangle, where you should know that opposite sides are equal in length, so what we have to do with that one is actually add the four sides together to give an answer 6 root 7. Part B has an isosceles triangle. I know it's isosceles because of the dashes on those two side lengths. So the other side that's got a missing side length would be equal to also 3 root 6, adding those three sides together, gives us an answer 7 root 6cm. In this example, we're going to have a look at mode and median. A quick reminder of what mode and median are. Obviously these two are the wrong way round, so let's fix that. So the mode is the number which appears the most often, and the median the middle number in a sorted list. Let's have a look at some surds. Now these surds are already ordered into a list in ascending order. So in order to find the mode, we're looking for the surd which appears the most often. We can see from this list it would be 5 root 7. So that would be our mode. The median, we're looking for the middle number. Well if we look to identifying which surd is actually in the middle of this list, we can quite clearly see that it would be the 6 root 7. So that would be our median. Here's the next set of questions for you to try. Pause the video to complete the task, and resume the video once you're finished. Here are the answers. In part A, I must find the mode of the cards. So I'm looking for the number which appears the most often. That would be 7 root 11. In part B, I've got to find the median, so I've got to sort that list of cards into either ascending or descending order, and once I've done that to find the middle number, that would be 7 root 11. In part C, the total of the cards, I would add all those cards together, to give a final answer 37 root 11. That's all for this lesson. Thanks for watching.

Which number is not a surd?

Simplify 6√7+5√7

A piece of wood has been cut up into three equal pieces as shown. What was the original total length of the piece of wood?

Add two surds

In this lesson, we will  learn how to add two or more surds where no prior simplification is needed.In these cases, the surds will all have the same root.

Maths

Y10 Maths (Higher)

Key Stage 4

Year 10

Y11 Maths (Core)

Year 11

Adding surds

Number (N)

THEME

UNIT

Subtract two surds

Add two surds where you need to simplify

Subtract two surds where you need to simplify

Simplify 6√2 - 4√2

Simplify 6√7 - 5√7

A piece of wood is shown. It is 7√5 m long. A piece of length 2√5 m is cut away. How long is the piece of wood now?

Lesson overview:Add two surds

Core Content

Adding surds: