Lesson video

Hi, I'm Mr. Chan.

And in this lesson, we're going to learn how to subtract two surds.

When subtracting two surds, we can subtract surds when they're like.

Here's a couple of examples.

In question one, six root three subtracts two root three.

We could see that the number inside the root symbol, they're the same so we can subtract these to get an answer four root three.

In question two, again inside the root symbol we have the number five.

So those two surds alike, we can subtract those.

Eight root five subtract three root five, we will get an answer five root five.

Here's a couple of example, where surds that are not like and we cannot actually subtract them.

In question one four root seven subtract two root three.

Those two surds are not like, so we cannot subtract those.

In question two, root 25 subtract root five.

Well, we can't subtract those because they're not like.

However, we do know that root 25 equals five, so we should simplify where necessary and the answer five subtract root five Here are some questions for you to try.

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

Here are the answers for question one.

There were only two questions that were false.

And those were question A and question D.

In question A those two are not like surds, so you cannot subtract them.

However, you can simplify root four further, root four equals two.

So the answer to that one would be root seven subtracts two.

In question D, again root 16 and root nine are not like surds, so you cannot subtract those.

However, you can simplify root 16 and root nine further.

Root 16 equals four root nine equals three.

So that question becomes four subtract three, the answer one.

Hopefully you did okay with those.

Here are some more questions that you can try.

Pause the video to have a go, restart the video once you're finished.

Here's the answers to question two.

In part A, four root three subtract two root three, you get the answer two root three.

In part B, seven root five subtract six root five, you get the answer one root five.

However, you don't normally write one root five just leave the answer as root five.

In part C, again they're like surds root 17 in both surds, so four root 17 subtract two root 17, you get the answer to 17.

Question D, the answer is six root two.

In part A, you'll notice in part A there actually three surds you're subtracting.

So just treat those in order, 14 root five subtract three root five first, that gives you 11 root five.

And then finally subtract the three root five.

11 root five subtract three root five gives you eight root five as an answer.

In part F, two root two subtracts eight root two you're subtracting a larger root from a smaller root in this question so you do get a negative answer.

Hopefully you got that correct.

In this example, we have James and Sue who each have a pencil.

James' has pencil is six root five centimetres long Let's hope that Sue's pencil is two root five centimetres shorter.

And we have to figure out how long Sue's pencil is.

We can do that using the subtraction calculation, by subtracting the difference from James' pencils length.

So we can calculate Sue's pencil by doing six root five, subtract two root five.

As these two surds are alike, we're allowed to subtract them, so we get an answer 45 centimetres long.

Here's a question for you to try.

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

Here's the answer for question three.

In this question, we're told that the smaller bar is three root five centimetres shorter than the longer bar.

So in order to find the length of the shots of bar, we're going to have to subtract that length away from the longer bar.

And the calculation becomes nine root five subtract three root five.

And if we do that calculation, we get an answer for the length of the shorter bar of six root five centimetres.

Here's a reminder about the mode and the median, where the mode is the number which appears the most often.

And the median is the middle number in a sorted list.

Now, we may get asked questions about the range, because that involves subtraction calculation.

To calculate the range, we work out the greatest number, subtract the smallest number in our list of numbers.

So here's some surds.

As we can see all those surds are alike.

So in order to calculate these three values of mode, median, and range, we can quite clearly see that the number which appears the most often, the mode is five root three.

Because they're already sorted, the middle number, we can see six root three.

Now, in order to calculate the range, I would have to find the greatest number.

In this case, 13 root three.

Subtract the smallest number, five root three.

That would give us the range.

So 13 root three, subtract five root three, we would get eight root three.

Here's a question for you to try.

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

Here are the answers.

In party A, you're asked to find the mode of the cards.

So the number appearing most often would be three root seven.

I can see two of those.

In part B, I hope you remember two surds of our list of cards out.

So what you're looking for is the middle of those numbers.

Once they're sorted.

And you will find once you've done that, the answer would be four root seven.

In part C, we're looking for the greatest number, subtract the smallest number.

Well, once you've sorted then you can quite clearly see that the largest number there would be 15 root seven, the smallest number three root seven.

Subtract three root seven away from 15 root seven.

You would get the answer.

12 root seven.

Hope you did okay on those.

That's all for this lesson.

Thanks for watching.