Lesson video

Hi everyone.

My name is Ms. Khu and today we're going to have a really interesting and fun lesson.

I'm so happy to be learning with you today and it might be hard in places, but I will be here to help.

You're going to come across some keywords that you are familiar with, as well as some new keywords to build on that previous knowledge.

It's going to be a great lesson and I'm really happy to be learning with you today In today's lesson, from the unit properties of number, factors, multiple squares and cubes, we'll be looking at powers and roots using a calculator.

By the end of the lesson, you'll be able to use keys for squares and other powers and square root on a calculator.

So let's have a look at some keywords.

The first keyword we'll be looking at is evaluate and evaluate means to find the value of a numerical or an algebraic expression.

For example, if we're asked to evaluate a hundred, divide by two, add five, this means we just need to find the value, which works out to be 55.

Another example would be if we're asked to evaluate the square root of 64, add two cubed.

Well, the square to 64 is eight, add two cubed is eight, so this gives us a value of 16.

So evaluate simply means to find the value of a numerical or algebraic expression.

Our lesson today will be broken into three parts.

The first part states that we'll evaluate using square and square root buttons.

The second part states that we'll evaluate using exponents, and the third part states that we'll look at the 10 the power of x button on our calculator.

So let's have a look at the first part of our lesson, where we will evaluate using square and square root buttons.

There are lots of different scientific calculators out there, but all have very similar functionality and notation.

I'll be using the Casio ClassWiz.

Now what I want you to do on your scientific calculator is find a button similar to this.

For me, it's a white square with an exponent of two.

You might have an X with an exponent of two.

This is the square button and it will square the number you input.

For example, if we're asked to evaluate five squared, how do we use a calculator to work this out? Well, all we need to do is press five, then press the square button and then simply press execute or okay, and it'll give you the answer of 25.

The great thing about scientific calculators is how the calculation will look exactly the same on your calculator.

So we know here the answer is 25.

Now let's have a look for this button on our calculator.

Hopefully, you know this is the square root button and it finds the square root of any number.

For example, if we're asked to evaluate the square root of 3,136, what we need to do is simply press the square root button, insert the digits 3136 to represent 3,136 and press execute or okay, same again.

The great thing is the calculation looks exactly the same on the calculator, thus giving us an answer of 56.

Remember the inverse relationship between square and square root.

For example, 1.

56 squared is equal to 2.

4336, and if you were to square root 2.

4336, it gives you the answer of 1.

56.

I really wanted to stress the inverse relationship between square and square root, and it's important that you know where those buttons are on your calculator.

It's also important to note that not all square roots of a number will be an integer.

Only the square root of a perfect square will evaluate to an integer.

For example, 12 squared is equal to 144.

This means the square root of 144 is 12.

We know 144 is a perfect square, so that's why it evaluates to an integer.

Now let's move on to a check.

Here we're asked to fill in the missing numbers using your calculator, and if your answer is a decimal, ensure you write down all the digits from your calculator display.

A, wants you to evaluate 4.

7 squared, B, wants you to evaluate 5.

4 squared at 2.

3 squared.

C, wants you to evaluate the square root of 2.

25, add 23 squared and D, well, we don't know what this number is, but we do know the exponent is two add 1.

4 squared is equal to 74.

21.

See if you can work these out and press pause if you need.

Well done.

So let's go through these answers.

Well, you should have got 22.

09 for A, 34.

45 for B, 530.

5 for C, and for D it was 8.

5 squared and 1.

4 squared is equal to 74.

21.

D was a very good question, so well done if you got that one right.

Now let's move on to our task.

Question one wants you to evaluate the following, if the answer is the decimal, please do write all the digits from your calculator display.

A says, evaluate 3.

45 squared.

B says, evaluate 1.

2 squared at 13.

4 squared.

C wants you to evaluate the square root of 76.

7376 subtract 2.

3 squared.

D wants you to evaluate the square root of nine squared at 12 squared and remember the calculation should look exactly the same on your calculator.

See if you can give this a go and press pause if you need.

Well done.

So let's move on to question two.

Question two states that we can use a calculator to work out the missing lengths of the following shaded areas.

Each shape is a square.

So the first part of the question states we have a square and it has an area of 127.

69 centimetre squared.

The second part gives us a square with an area 4.

6225 metres squared, and the third gives us an area of 0.

000001 metres squared and we have to work out the length of each of our squares.

See if you can use your calculator to work out those missing lengths and press pause if you need.

Well done.

So let's move on to our third question.

Question three says, using a calculator, we must explain why the following, evaluate to the answer given.

3A, shows the square root of a square root of a square root of 65,536 evaluates to four.

Can you explain why the answer is four? For B, it says the square root of 53 squared is equal to 53.

Could you explain why the answer evaluates to 53? See if you can give it a go and press pause if you need.

Well done.

So let's go through these answers.

For question 1A, you should have got 11.

9025.

For 11B, you should have got 181.

For 11C, 3.

47 and 11D should have given you a nice 15.

Remember, each of the calculations should look exactly the same on your calculator display.

For question two, we're given the area of each square, so we need to find out what is the length of each square.

Hopefully you spotted, you square root in order to find the length.

So the square root of 127.

69 gives me a length of 11.

3 centimetres.

The square root of 4.

6225 gives me a length of 2.

15 metres and the square root of 0.

000001 gives me a length of 0.

001 metres.

Well done If you spotted, we're using the square root as it's the inverse of square.

For question three, you are asked to explain why the following evaluates the answer given.

Well, for question 3A, what we have here are three square roots.

The question means you're square rooting the 65,536 to make 256.

Then the square root of 256 is 16 and then the square root to 16 is four.

So that's why when you square root the square root, the square root of 65,536, the answer is four.

For B, I'm hoping you spotted the square and square root are inverse of each other, thus they cancel out, leaving us with the 53.

Well done.

So let's move on to the second part of our lesson where we'll evaluate using exponents.

Going back to our calculator, I want to see if you can find this button.

This button is the power off button and means we can insert a base and an exponent.

For example, if we were asked to evaluate 137 to the power of four, what we need to press is the 137, then the power button, then the four and press execute or okay.

The great thing is the calculation will look exactly the same on your calculator display.

This gives us a huge answer.

So you can see why we use powers and exponents opposed to writing out the numerical value.

When you using the power button, it's very important that you're able to scroll out of the power button using the cursor keys.

When inserting a calculation, scrolling to the right enables you to exit that power function.

So let's have a look at what I mean.

If the question wanted you to evaluate two to the power of five, add three to the power of four.

What you have to do is insert two to the power of five and then you'll see that on your calculator display, but you need to scroll out by pressing the right cursor, so you come outta that exponent function, then you simply add three, press the power of button, four and execute.

This will show the answer to be two to the power of five, add three to the power of four on your calculated display, giving 113.

Scrolling to the right is important, as it enables you to leave an operation or a function.

Now let's look at a check question.

I'll do the first part and I'd like you to try the second part.

The question wants us to evaluate the following, ensuring we write all the digits on our calculator display.

We have 3.

2 cubed, add 1.

2 to the power of four.

While inserting this into our calculator, I'm gonna go, I'm going to explain button by button.

3.

2 power of three, so you should see 3.

2 cubed on your calculator screen.

Then you scroll to the right, because we need to leave that exponent function.

We add 1.

2, press the power button, four.

This will then show the calculation exactly as you see here.

3.

2 cubed add 1.

2 to the power of four will be shown on your calculator display.

You can press execute or okay, and it'll give you an answer of 34.

8416.

You may have discovered your answer is not in a decimal form.

So when the calculation is left on the display of the screen, all you need to do is press the format button and then down, see if you can find the decimal form and press execute.

This will then convert your answer into a decimal form if it doesn't do that automatically.

Now let's see if you can try a question.

The question wants you to evaluate the following, ensuring you write all the digits from your calculator display.

Eight to the power of four divided by four cubed add 2.

1 squared.

What buttons do you need to press in order to work out the value of this numerical expression? See if you can give it a go and press pause if you need.

So I'm going to go through this button by button.

What you should have pressed is eight power button four.

Scroll out of that exponent function, then divide it by four, power of three.

Once again, scroll to the right to leave that exponent function.

You add 2.

1 and then access that squared.

You may have chose the power of and then the two button, which is exactly the same.

Once you press execute, it should give it to you as a decimal.

If not simply press format, press down and then okay or execute.

This will give you a final answer of 68.

41.

There are lots of calculator skills involved in this question.

A huge well done if you've got this one right.

Now let's have a look at your task.

The task wants you to evaluate the following, and if your answer is a decimal, write down all the digits from your calculator display.

Remember to press that format button and find the decimal form.

1A wants you to work out four to the power of six, subtract six to the power of four, B, wants you to work out 27 to the four divided by nine squared divided by three to the seven, C, wants you to work out 4.

2 cubed divided by two to the power of four and D, wants you to evaluate the square root of three to the four, add four to the three, add five squared, subtract one to the seven.

Remember each calculation should look exactly the same on your calculator display.

See if you can give these a go and press pause if you need more time.

Well done.

Let's move on to the second question.

Question two shows Sophia followed this function machine and her input was 27 and her output was 730.

She knows that the function machine states the input needs to be put to the power of four, then we add three to the six, and then we divide by nine to the three.

Which of the following buttons did she press to get the right answer? Do you think it's A or B? Press pause to give it a go.

So let's go through our answers.

For question 1A, you should have got the answer of 2,800.

For question 1B, it was simply three.

For 1C, we have 4.

6305, and for D, it's 13.

Really good calculator skills, if you've got any of those right.

Let's have a look at two.

Well hopefully you spotted it's A.

Well done if you got that one right.

Now let's move on to the last part of our lesson.

The last part of our lesson uses 10 to the power of X button in our calculator.

This is a really handy button to use.

Simplifying in mathematics is really important and we multiply numbers with a base of 10 a lot in mathematics and in science.

It's such an important base that it has its own button.

You might be able to see it here.

This allows us to quickly evaluate when we multiply a number with a base of 10.

So for example, if we're asked to evaluate 2.

1 times 10, times 10, times 10, times 10, times 10, (exhales) it's easier for us to simply write 2.

1 times 10 to the five.

Now we can insert it onto our calculator as 2.

1 times 10 to the power of five and then press execute.

This will then give us an answer of 210,000 and once again, the great thing about scientific calculators is that the calculation is displayed exactly the same on the calculator.

Alternatively, we could simply type it in as 2.

1, press that times 10 to the power button and then five and we get exactly the same answer.

The display on the calculator will be the same.

This is just a quick and easy way to get our answer.

Let's have a look at 3.

5 times 10 to the four, add 1.

3 times 10 to the five.

We could input it the long way, 3.

5 times 10 to the, press the power of button four.

Then scroll to the right, add 1.

3 times 10, press that power off button and five and then execute.

This will give us an answer of 165,000.

It looks on our calculator screen exactly how we see the calculation.

Alternatively, we can simplify our calculation by simply pressing 3.

5 that times 10 to the power of button four.

Scroll to the right to exit the exponent function, add 1.

3 times 10 to the power of button, then five.

It still gives us exactly the same answer, but we're pressing glass button and simplifying what we're inputting into the calculator.

So let's do a quick check.

Which the following is the correct evaluation of 5.

76 multiplied by 10 to the five? See if you can find it out and press pause if you need.

Well done.

So hopefully you've got it's 576,000.

Now let's move on to the task where you are asked to evaluate the following.

Question 1A wants you to evaluate 1.

7 times 10 to the four, B, wants you to evaluate 3.

9 times 10 to the eight, subtract 2.

6 times 10 to the seven, C, wants you to evaluate 1.

2 times 10 squared, add 1.

2 times 10 cubed add 1.

2 times 10 to the four.

See if you can give this a go and press pause if you need.

Great work, so let's move on.

Work out the missing exponents, 2.

5 times 10 to the what, add 3.

5 times 10 to the what, gives you 285,000? For question B, 6.

3 times 10 to the what, add 2.

8 times 10 to the what, gives you a huge number of 63 million and 280,000 and for C, 3.

1 times 10 to the what, subtract 2.

7 times 10 to the what, gives you this massive number, 3,099,730,000.

See if you can work out those missing exponents.

Well done.

So let's go through these answers.

For question one, here are our answers.

1A should have been 17,000.

For B, this is 364 million, and for C, it's 13,320.

Well done.

For question two, you should have got the following exponents.

For A, we had a five and a four, for B, a seven and a five and for C and nine and a five, that was really tough, so well done if you got any of those right.

In summary, evaluate means to find the value of a numerical or algebraic expression.

Scientific calculators generally have the same functionality and same notation.

So here you can see for the Casio ClassWiz, this represents the square button and it will square the number.

This is the square root button and it finds the square root of any number.

The power of button is indicated here where it allows us to insert the base and the exponent, and our last button allows us to quickly multiply a number with a base of 10.

Massive well done today and I hope you've enjoyed this lesson.