Which calculation can be simplified further?

Simplify √12 + √27

Simplify fully 3√8 + √50

Add two surds where you need to simplify

﻿Hi, I'm Mr. Chan and, in this lesson, we're going to learn how to subtract two surds where you need to simplify. In this example, we've got the question 7 root 5 subtract 3 root 2, now, these two surds are not alike, so in this example, we cannot actually subtract these two surds one from the other. So, we would leave the question unsimplified, and we cannot simplify any further. Let's have a look at another example, root 50 subtract 3 root 2. It looks as though these two surds are not alike, however, we can think about simplifying root 50 further, as so, simplifying root 50, we could write root 25 multiplied by root 2, that simplifies to 5 root 2. So, how we proceed with this question, is simplify root 50 into 5 root two subtract 3 root two, now, we have two like surds, which we can subtract to give a final answer two root two. Here are some questions for you to try. Pause the video to complete the task, resume the video once you're finished. Here are the answers, question one gives you a little bit of practise simplifying surds. So, root 8 simplifies to 2 root 2, root 12, simplifies 2 root 3, and root 50 simplifies to 5 root 2. Hopefully you got those correct because they do help you with question two. So, in question two, 2a, 5 root 2 subtract root 8. Well, you've simplified root 8 already in question one, so the question becomes 5 root 2 subtract 2 root 2, that gives you an answer 3 root 2. In 2b, you've already done root 12 in question one, so it's a matter of simplifying root 48 and that equals 4 root 3. So, the question becomes 4 root 3 subtract 2 root 3. To give you an answer 2 root 3. In question 2c, you've already simplified root 50 in question one, so let's look at root 32. Well, root 32 simplifies to 4 root 2. So, the question becomes 5 root 2 subtract 4 root 2 to give you 1 root 2 and we wouldn't normally write the 1, so we just leave the answer, root 2. Let's have a look at a part whole model example. A part whole model takes a whole number, and splits it up into two or more parts that add together to make the whole number again. So, in this example, we see the number 12 split up into two parts, one part being 7. I can figure out what the missing part is by doing a subtraction calculation like so, 12 subtract 7 gives us 5, that tells us that the missing part is 5. Now, applying this to surds, we've got a whole part of 5 root 3 that's been split up into a part, root 12 so, in this example, we have to figure out what the missing part is. And, again, we could do a subtraction calculation to help us like so, 5 root 3 subtract root 12. Looking at that, they're not like surds, but we can simplify root 12 further into 2 root 3. Now, we have like surds that we can subtract to give a final answer, 3 root 3. Here are two part whole model questions for you to have it go out at. Pause the video to complete the task, resume the video once you're finished. Here are the answers, in part a, we're going to have to figure out what's missing in the part whole model by doing a subtraction of 7 root 5 subtract root 20, those are not like surds, so we're going to have to simplify those first 7 root 5 subtract root 20, well, I know that root 20 when I simplify that is 2 root 5. So, the calculation becomes 7 root 5 subtract 2 root 5. That gives me an answer 5 root 5. And that's the missing number in the part whole model. In part b, this is slightly trickier because we have to simplify 2 root 72, and also root 50. So 2 root 72 simplifies to 12 root 2 and root 50 simplifies to 5 root 2. So, we get a calculation to figure out the missing number, 12 root 2 subtract 5 root 2 that gives us the missing numb value, 7 root 2. Here's another question for you to have a go at. Pause the video to complete the task, resume the video once you're finished. Here's the answer, in this question, we're told that the width of a rectangle is root 108 centimetres shorter than its length. The length being, as shown, root 300 centimetres. And we're asked to figure out what the width of the rectangle is. So, to work this out, we would have to subtract root 108 from root 300. We're going to have to simplify those surds first. And once we do that, we'll get the calculation root 300 simplifying to 10 root 3 and root 108 simplifying to 6 root 3. So the question becomes, what is, 10 root 3 subtract 6 root 3? And we get the answer, 4 root 3 centimetres. In this example, we've got a reminder how to calculate the range. We do that by working out the greatest number, subtract the smallest number. So, let's have a look at some numbers. Here, we've got some surds, now, looking at those surds, they're not alike, so in order to subtract them we're probably going to have to simplify. And after we've done that, we're going to get this. So those surds now are alike, if we find the greatest number, 6 root 2, find the smallest number 2 root 2, we can work out the range by subtracting them from each other, 6 root 2 subtract 2 root 2, we get a final answer, 4 root 2. Here's a question for you to try. Pause the video to complete the task, resume the video once you're finished. Here are the answers, in part a, you're asked which card will simplify to 6 root 5? And that is, in fact, root 180. In part b, root 100 is not classed as a surd because that simplifies to 10, root 100 equals 10. And in part c, working out the range for the cards, well, we know that range is the greatest number subtract the smallest number so, with this question, we're subtracting root 200 subtract root 8, which gives us when we simplify a calculation of 10 root 2 subtract 2 root 2, to give an answer 8 root 2. Hopefully, you got those correct. That's all for this lesson, thanks for watching.

Simplify fully √27 - √12

Simplify fully 4√3 - √12

Subtract two surds where you need to simplify

In this lesson, we will learn how to subtract two surds where you may need to simplify at least one surd prior to subtracting.

Maths

Y10 Maths (Higher)

Key Stage 4

Year 10

Y11 Maths (Core)

Year 11

Adding surds

Number (N)

THEME

UNIT

Add two surds

Subtract two surds

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?

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?

Lesson overview:Subtract two surds where you need to simplify

Core Content

Adding surds: