Lesson video

Yeah, I'm just doing this lesson.

Oh! Hi everyone! This lesson is about expanding single brackets with Surds.

Hi everyone, this is a lesson that builds on our understanding of multiplying surds.

Here, we are asked to expand and simplify an expression.

First of all, expand means to multiply.

So, let's multiply the square root of two, by the square root of seven, and then lets multiply the square root of two, by the second term, inside the bracket which is nine.

There you go! We've expanded, and simplified.

Let's expand and simplify the second expression we are given What's different to the first expression? Do you see? There are two identical surds.

First of all, let's multiply the square root of nine by 11.

And then let's multiply the square root of nine by itself.

That will give me an integer answer, of negative nine.

All together, expanded and simplified, my expression is 11 the square root of nine, minus nine.

Let's put that into practise, here are some examples for you to try.

Pause the video, and return to check your answers.

Here's the solutions to question number one.

Remember, in question one E, you had to simplify.

The square root of 16, is four.

Let's have a look at a different example.

Expand and simplify, the square root of two, in brackets, the square root of eight plus five, and then outside of brackets, plus four.

The addition of four, makes this more complicated than the previous examples we've looked at.

Good, let's leave that to one side.

First of all, expand your brackets.

Don't forget to add on the four.

And then we're going to simplify.

The square root of 16 can be simplified to be four.

Collect our like terms together.

Eight plus five lots the square root of two.

Job done.

Here are some examples for you to try.

Pause the video, and return to check your answers.

Question two E I've shown here, that the square root of 12 can be simplified, to two lots of the square root of three.

So, if you didn't quite get the same solution, maybe that's where you made a slight, not a mistake, but you haven't simplified from there.

Hopefully you did it good, yeah! Well done for getting this far, have a go at question three.

These are known as area models.

Multiply those surds together to find the answers, in the middle of your rectangles.

Pause the video, return to check your answers.

Here's the solutions to question number three.

Uh, yeah you are working with what are known as area models.

And, if you forgot to kind of bring your two terms together at the end, don't worry too much, because you might not have seen these type of examples before.

But that's what we were looking for in the end.

Two nice expressions with surds.

Here are some more questions for you to try.

Pause the video, and return to check your answers.

Here's the solutions to questions number four.

We all love a good surd.

Questions four A and B, were the final questions, and hopefully by now, you're getting some kind of fluency.

Take your time with surds.