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Hello everyone I'm Mr. Lund and this lesson is on higher roots.

Calculate five raised to the power of four.

That means multiply five by itself four times.

We can make this easier by multiplying the first two numbers together that finds us an answer of 625.

How do we find the fourth root of a number? Well, if five to the power of four is equal to 625.

That means that the fourth power of 625 is the base number five.

It's a bit like saying which number did I multiply by itself four times to give me 625.

Well, your solution is five.

Here are some function machines.

If I have an input of A and I raise it to the power of five, my output would be A raised to the power of five.

If I put an input of B into my function machine, and I found the six root, my output would be the six root of B.

So my question to you is what number would go in here that I've raised to the power of seven that finds me an answer of C? Hopefully this shows you that the seventh root of C raised to the power of seven, equal C.

They are inverse operations.

One on those lead over.

Here are some questions for you to try pause the video and come back when do you want to check your answers.

Here are the solutions to questions one and two.

Question two B the fourth root of 16, the actual answer was two.

Do you see a pattern in questions two A, B and C? Here are some more questions for you to try pause the video and return when you want to check your answers.

Here are the solutions question number four and five.

Now finding higher roots of numbers can be very difficult, but the number 64 and 81 are both interesting examples and are often used in exams, especially as you move higher up in terms of your math skills.

Here are some more questions for you to try pause the video and return when you want to check your answers.

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

Question six C on your calculator.

You will find gives you an error.

The reason being that you cannot take an even root of a negative number.

Try questions nine and 10 pause video and return when you want to check your answers.

Here's the solutions to question nine and 10.

Question nine is quite a nice sequence.

When we take the square root of a number we don't write a two, we just forget about the two.

So it's a little bit of a confusing piece of notation that is hopefully highlighted in this sequence.