Lesson video

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Hi, everyone, I am Mr. Lund, and in this lesson we're multiplying two surds with coefficients.

When you multiply a surd and an integer, notice that the surd has a coefficient in front of it of two.

Here's what you would get three multiplied by two lots of square root of two is six, lots of the square root of two.

So with that knowledge, do you think this is true or false? It's false, you should have had a result of six lots of the square root of two again.

Right, let's multiply two surds with coefficients together let me show you an example.

I've highlighted the coefficients in blue, to emphasise the fact that this calculation is quite easy if you think of the coefficients and the surds, almost as separate calculations.

So if I multiply the coefficients, I get a six, and I multiply the surds, I get the square root three times by five.

Let's simplify that.

There's our result, six lots of the square root of 15.

With that knowledge, have a look at this question true or false? Square of two multiplied by five lots of the square root of three is equal to 10 lots of the square root of six.

Have you had time to think? It's true two times by five gives you 10 square root to two times by square root to three gives you the square root to six.

Combine them together.

There you go.

Let's move on.

Let me show you another example.

Two lots of the square root of three multiplied by the square root of three is equal to two lots of the square root of nine.

That is the same as saying two multiplied by three, if we simplify, that binds as an integer solution.

Watch out for that type of simplification.

What happens when we square a surd with a coefficient? Let's have a look.

So we've got two lots of square root to three, all squared.

That is equal to two lots of square root of three multiplied by itself that is four I've multiplied the coefficients together times by three multiplying the surds remember you just end up with three there is your solution a Nova integer solutions.

Splendiferous.

Here's the solutions to question number one.

How did he do? Remember multiply the coefficients and the surd separately and then combine them.

Now when working with surds, always remember to simplify.

In this example I should find I have an answer of three lots of the square to 12 But, the square root of 12 can be written as two lots of square root of three.

That gives me an answer of six lots of the square root of three.

Watch out when being asked to simplify surds in exam questions.

Here's an example which is very similar to the last example.

But, both surds have coefficients.

Follow the same rules that we have been doing.

Multiply the coefficients together, multiply the surds together, think of them as separate calculations.

Remember the square root of 12 can be written as two lots of square root to three.

So our solution should be 12 lots of the square root to three These examples will challenge your understanding of simplifying surds.

Here are the solutions to question number two.

How did you do with your simplification? It is a skill that requires some practise so here's some more example for you to try.

Here are the solutions to question number three.

How did you do? Remember when simplifying surds we need to look for factors of the numbers inside the surds that are square numbers.

And then we can factorise those outside of the surd.

Practise makes perfect.

Let's try a question four now.