Lesson video

Hello everyone, my name is Mr. Lund.

And this lesson is on multiplying two surds together and simplifying.

When you multiply a surd and an integer together, for example, 3 times the square root of 2, we would write this like so.

So here's a quick fire question, is this true or false? Yep, it's true.

What about this example, true or false? The square root of 9 times by the square root of 2 equals 3 lots of the square root of 2.

It is true.

Yeah, the square root of 9 can be simplified to be 3, so 3 times square root of 2 gives you that result.

When you multiply two surds together, you need to follow this rule, the square root of A times by the square root of B is equal to the square root of A times by B.

Let me show you an example.

The square root 3 times by the square root of 5 is equal to the square root of 3 times by 5.

That gives us query to 15.

So true or false, the square root of 3 times by the square root of 10 is equal to the square root of 30.

It's true.

What about this example.

What's the same and what's different with the last example.

All we've done is placed the square root of 10 and the square root of 3 in different positions, but the answer is the same.

When we square a surd, we find an interesting and important result.

So the square root of A multiplied by the square root of A, the same number notice, is equal to square root of A squared.

That is equal to A.

Squaring and square rooting are inverse operations of one another.

So let me show you an example.

Here, I'm going to multiply the square root of 5 by the square root of 5.

That is the same as saying the square root 5 times by 5, which equals the square root of 25.

Hopefully, you know, that just gives you the integer solution of 5.

So let me show you another example.

Here I have the square root 3, all squared.

That is equal to the square root of 3, multiply by 3, which is equal to the square root of 9, which finds you the integer solution of 3.

So square rooting and squaring, cancel each other out.

And that just leaves us with the number that was inside the square root.

So using our knowledge of squaring square roots, what's the missing number? There we go, 2.

5.

So let's move on.

When working with surds you must always simplify where possible.

So if I was to say the square root of 18 times by the square root of 2, well, that finds me the square root of 36, 18 times by 2, so it's 6 square rooted.

Don't forget to simplify that.

It finds you in integer solution of 6.

Here's an example which shows where you might need to simplify.

What about this the square root of 6 times by the square root of 3 is equal to the square root of 18.

Now the square root of 18 is the same as saying the square root of 9 times by the square root of 2.

That can be simplified to 3 lots of square root of 2.

So let's put what we've learned into practise.

Here's some questions for you to try.

Pause the video and return to look at your answers.

Here are the solutions to questions one and two.

There's a real nice variety within these questions.

Think about how they are the same and how they are different.

Let's try question three now.

Pause the video and return to look at your answers.

Here are the solutions to question three.

How did you get on? Factor pairs and knowing your factor pairs will be really useful to help you with these styles of questions.

If any of the factor pairs are square numbers, you know that you will have to simplify.

These examples will need simplifying fully.

Good luck, off you go.

Pause the video, return to look at your answers.

Here are the solutions to question four and five.

Well done for getting this far in.

When we square a surd it's like we undo what is being done to the number.

So the square root of A squared, we'll just find as the result of A.

Let's finish off with a question six A and B, well done for getting this far.

Pause the video, return to look at your answers.

Here are the solutions for question number six.

Don't forget that your units will be in centimetres squared.

The last question only gives you one measurement, but because it is a square, then all we need to do is square the square root of 130, finding us the solution of 130.

Well done for getting this far.