Simplify fully  √𝟕2

Who is correct?

Jack and Jill are arguing about surds. Jack says: √4 x √12 = √48. Jill says: √4 x √12 = 3√4. Who is correct?

Simplify √10 - √3

Simplify, if possible: √8 + √50

Which of the following is NOT a surd?

Simplify: 15√14 ÷ 3√2

Indices and Radicals Quiz

﻿Hello and welcome to this lesson on indices and power of zero with me Miss Oreyomi. For today's lesson you'll be needing a paper and a pen or something you could write on and with. So please pause the video now if you need to go get those. Also, if you can minimise distraction by putting your phone on silent and trying to get into a space with less noise then please do so and press play when you're ready to resume the lesson. Okay. let's start with your try this task. I am going to read the statement out for you. This is more of a thinking task. So you can actually get a piece of paper and try to work this out practically or you can just think about it. Anthony folds a piece of paper in half twice then unfolds it. It makes four rectangles. Cala folds a piece piece of paper in half three times and then unfolds it. It makes eight rectangles. Questions you're to think about. How many rectangles will be made by folding the paper in half. Four times? Five times? Six times? And then what if I don't fold the paper in half at all? Pause the video. Think about this question. Again, like I said, you could get a piece of paper and actually fold up the rectangles and see what you get. Or just think about it and then resume when you are ready to proceed with the lesson. Okay. Hopefully from your try this task you are able to deduce that it's linked with indices. If I have my folded sheet of paper. I've got a fold in half. And then I fold it in half again. Bearing in mind I am not great at drawing even straight lines. If I fold it in half again, how many rectangles do I have? Well, it would be four, wouldn't it? 1 2 3 4. I have a two by two sheet. Another way of saying that is two lots of two. If I've got two lots of two, that is saying two squared. Two squared is I'm multiplying two by itself two times. This is going to give me four. What if I want to split my already halfed rectangle into another half again. That will be that and that. Like I said, straight lines are not my thing. Now I've got 1 2 3 4 5 6 7 8. Two to the power of three is eight. Is essentially saying, I am timesing two by itself three times. And here I am timesing two by itself two times. If I want to label this two to the power three. What is the three known as? Well, it's known as power. It's known as the index. And it can also be known as the exponent. And this two here is known as the base. We're going to discuss this some more further down the lesson. But you just need to know that the three other top is called the power and then the two is called the base. Now we have a student here and she says, If I fold the paper in third two times I will get six triangles. Six rectangles rather because three times two is six. Do we agree with this student? How about you pause the video. Attempt this. If I fold the paper in 32 times she would get six rectangles. Is she correct? Well, hopefully you said no. Because if I fold my rectangle into thirds. I'm going to do it again because this is really... If I fold my rectangle into thirds again how many rectangles do I now have?? That's a neater version of what I'm trying to do. I now have 1 2 3 4 5 6 7 8 9. Our student here is wrong because I've folded each rectangle I started wIth. I started with 1 2 3 I've folded each one into three. I now have nine. Folding it into three twice is the same as multiplying three by itself. I have three times three which is nine. Because here I have three lots of three. Are you starting to see a pattern? What if I fold my paper now into three? If I fold my paper in third three times how many rectangles without will I now have? If I fold my paper in thirds three times how many rectangles would I have? Hopefully you said 27. Because it would be essentially the same as saying three times three times three. Also, if you want to show it by splitting each now rectangle into thirds again, you would see that you have 27 rectangles. If I have two to the power of three I know is two times two times two which is the same as eight. Two to the power of four is two times two times two times two which is 16. Hopefully, you're starting to see that every time I multiply my two to the power of something I am just timesing in my previous power by two. I'm timesing my previous number by two. Two to the power four to two to the power five. I times 16 by two and I get 32 From two to the power of three which is eight to two to the power four. Because I have added one, I'm going to times it by two once. What if... What do you think two to the power of six will be? Well, is going to be the same as going 32 times two. Isn't it? Which is going to be 64. What if I want to go from two to the power of six to two to the power of five. If I know my value for two to the power of six and I want to work up my value of two to the power five. Well because I'm decreasing my power by one I am going to divide 64 by two to get 32. Likewise, if I'm going from two to the power five and I want to work up to the power four I would divide 32 by two to get my two to the power four value which is 16. Right. Let's think about this. Anthony Folds a piece of paper in half twice and then unfolds. It makes four rectangles. What if he doesn't fold his paper at all? Remembering that we're starting with this rectangle. If he doesn't fold his paper at all how many rectangle does Anthony have? Hopefully, you said one. Essentially anything to the power of zero is one. Regardless of whether if... Because he did not Fold his rectangle but it still has that initial rectangle. That one rectangle. It is one. If I say 555 to the power of zero that is one. 1001 to the power of zero that is one. Any number, any value to the power of zero is one. You're now going to get a chance to work for your independent tasks using all the skills that we've learned in today's lesson so far. If you see a question that you don't understand try to think about it logically and you'll probably get the answer that way. Attempt all the questions on your sheet and then resume the video. And we would go for the answers together. Pause the video now to go through your questions. Let's go for the questions now. I've got three squared which is nine. So I'm doing this first and then I'm timesing that by three because I've got nine to the power of three. Okay. If you remember order of operations remember we always do what's in the brackets first before we move on to working on the indices. I am working on my brackets first. Three squared is nine. Nine times nine times nine gives me 729. Okay. Again, I'm doing what's in the bracket first. The square root of four is two. Two squared is four. Remember that anything to the power of zero is one. This time I am doing two to the power of four. That is 16 times by nine. . If I do that root of 16 is four and root of nine is three. My answer should be 12. For this one we I seven times 25. And that gives me 175. Next one. I've got 17 subtract 49. Because my..... The number I'm subtracting is bigger than the number I started with. Then therefore I will have a negative number. My answer is negative 32. Anything to the power of zero even if it is a negative number is one. 76 to the power of one is 76. Because if I do two to the power of one. I'm timesing two by itself once. That is two. Say 76 to the power of one is 76. Subtract 76 to the power of zero which is one. My answer is 75. Okay. Next one I've got 300 subtract four to the power of four. That's four times four times four times four. That is 256. 300 takeaway 256 that is 44. Next one. Five cubed is 125. Subtract from four cubed which is 64. My answer is .... 61. I hope the task that is straightforward enough for you. If you struggled with some of them just go over the video again and just make sure that, you know? You recap and fully understand what's happening here. Okay. We're moving on to explore task where a question has an x say number one. Find the lowest possible integer. The lowest possible entity that would make the statement true. And where question has a y, find the highest possible integer that would make the value true. The statement true. For the first one. Two to the power of something. The lowest possible number that two to the power could be raised to. That the answer would be greater than 10 to the power of one. Well I know that two to the power of three is eight so it can't be eight. What would be the smallest possible integer value that two can be raised by so that my value, my answer is bigger than 10? Pause the video now and attempt your explore task. Okay. We've now reached at the end of today's lesson. I hope this lesson helps you to consolidate your knowledge on indices. And also know that anything raised to the power of zero is always one. Before you leave, do complete the quiz just to show yourself what you've learned from today's lesson. And also just to again consolidate your learning on indices. And I will see you at the next lesson.

Hint: Work out the value in the brackets first.

Indices and power of 0 Quiz

In this lesson, we will recap our knowledge of basic indices. We will explore the power of zero, and carry out calculations involving low power values.

Lesson overview:Indices and power of 0

Core Content

Indices and standard form: