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Hello, everyone.

I'm Mr. Lund.

Today's lesson is on square and cube roots.

A square root is the inverse operation of squaring a number.

So let's square the number four.

Four squared equals 16.

That means that the square root of 16 is equal to four.

It's a bit like saying, well, which number did I multiply by itself to find me a solution of 16? Negative four squared also equals 16.

Mm-hmm! So does that mean the square root of 16 is equal to negative four? Well, yes.

Negative four and four are both possible solutions.

So when you take square roots of numbers, there are two possible solutions.

The square root symbol refers to the positive square root.

If you wanted to include the positive and negative roots, you would write using this symbol.

Here, we are asked to calculate the cube root of 125.

The cube of the number five is equal to 125.

So the cube root of 125 is equal to five.

It's like it's asking you to say which number did you multiply by itself three times to find 125? In this case, that number was five.

Here's a second example.

Can you calculate the cube root of a negative number? Yes, you can.

If I was to find the cube of negative five, that would equal negative 125.

So the cube root of negative 125 is equal to negative five.

So here are some questions for you to try.

Pause the video.

When you're finished, come back and look at your answers.

Here are the solutions.

In question one, there is a rather complex idea.

You cannot take the square root of a negative number.

See what happens if you try that in your calculator.

Let's try questions three, four, and five.

Pause the video, and come back when you want to check your answers.

Here's the solutions for you.

In question four and question five, they're asking you to follow the same operation.

But one uses notation, and the other uses the English language.

In maths, it is important to be able to understand the notation and the language that we use to describe that.

Here's some more questions for you to try.

Pause the video, and return when you want to check your answers.

Here are the solutions to questions six, seven, and eight.

Notice, whenever you take the cube root of a negative number, you end up with a negative solution.

Well done for getting to these last questions.

Pause the video, and return when you want to check your answers.

Keep going.

Here are the solutions to questions nine and 10.

Question 10 seems a little bit tricky.

But if you take each one individually, so the cube root of 27, think of that almost like on a separate page, work it out, and then go back to the next part of the question.

Sometimes that helps you to unpack the problem.