Hello, I'll talk about squares and square roots!
What to expect today we will be talking about squares and square roots.
So what is squaring a number let me show you an example here is squaring a number 4 raised to the power of 2 is also called for squared basically anytime you have an exponent of 2 you are squaring the number so that's that's pretty straightforward.
Exponents before four to the power of two means four is our base and two is our exponent so we multiply 4 times itself two times right four times four gives us 16
Now why do we call this squaring a number so let's go ahead and I'm going to show you Real quick below is a square if I had the length of four from one side to the other and I was too square this number it would look like this see I've multiplied 4 x 4 if you count their 16 squares inside of there so that's why we call it squaring because that would be how you would find the area of a square that has a length of four all right That's just kind of a side note, you don't really need to know about that, I just always wondered why to was squaring when it seems like a funny number to call it squaring something, but that's why because 4 to the power of 2 is like finding the area of a square and as a side length of four
All right, let's go ahead and actually do some squaring remember we talked about exponents this is our base 6 that's our exponent 2 and so that we means the base times itself two times the most common mistake is for people to just multiply 6 times 2 equals 12 and that is wrong it's the base number times itself so let's practice doing that.
Five squared that's an exponent form when we expand it out it becomes 5 times 5 which is 25 so here are three forms exponent form expanded form standard form that's how we solve an exponent it's when you get quicker at it you'll probably go straight from exponent form to standard form, but as you're learning about squaring you probably want to write it out in the expanded form just to remind you what an exponent means.
let's do it one squared. 1 squared means 1 times 1 which gives you the answer of 1.
2 squared is 2 times 2 which is for remember two times two is because the base is being multiplied times itself not because you're multiplying the base times the exponent that one can be Confusing.
3 squared which is 3 x 3 and that gives you nine so you can continue going to make a whole list of Squares.
I'm going to go ahead and do that for you so here's the list of perfect squares one two three four five and six these are the ones we've worked with already inside of this lesson so you can see these perfect squares I'm going to show you the of the next six I would encourage you to memorize these ones as you go it's easy to make a list of your own Perfect squares alright, you simply multiply the number times itself and it will give you a list of perfect squares so below is a list of perfect squares.
I would encourage you to memorize have those down and one of the main reasons you want to memorize that is because you're going to need to know them when you get into the second half of this lesson which is square roots.
knowing the math - Squares and Square Roots
The square root is the opposite of squaring so below is an example the square root of thirty-six is six means what number times itself Gives us 36 while six does 6 times 6 is 36.
Look at some more the square root of 81 is nine times nine is nine or nine squared equals 81 the square root of 49 is 77 times 7 is equal to 49
I've got done three questions here and I'd like you try them out yourself!
Hopefully you were able to find that the square root of one is one the square root of 144 is 12 in the square root of 25 is 5 those are square roots what number times itself will give me the number inside of that symbol ok that's what a square root is.
Here is just like my list of perfect squares I have a list of square roots for you I would encourage you to memorize these these are ones that you will see over and over and over all of the questions are going to be based on these twelve numbers So I would memorize the list of perfect squares and they're square root companions that go along with them that Would be a really good way to remember these and to make sure that you get them and they'll become quick I'm sure you already have some of them memorized already.
Quick recap squaring a number means raising it to the power of 2 and taking the square root of a number is the opposite of squaring it so 3 squared equals nine the square root of nine is equal to three hope that lesson was helpful for you.