WEBVTT
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Hey, this is Professor Perez from Santa Back College.
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Today we're going to work on square roots.
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Don't get scared.
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Anyway, before we get started, we're going to get Charlie out.
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He's going to be radio.
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Hey, Charlie, you ready to go?
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Yeah, we're doing square roots today.
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That's right.
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These problems are radical.
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Anyway, let's get started here.
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Right there.
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Okay, pay attention, Charlie.
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What number do we square to get 16?
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Four.
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That's right.
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You just did a square root.
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What?
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Anyway, well pay attention, Charlie.
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If somebody asks you what number do we square to get 16?
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It's four because four squared is 16, but it is also negative four because negative
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four squared is 16, right?
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Okay, now let's talk about the square root.
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What is the square root of 16, Charlie?
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Well, watch this.
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We have a 16 and we have a radical symbol there.
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That radical symbol with a 16 underneath is saying what is the square root of 16?
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So when somebody asks you what is the square root of 16, you're thinking what number do
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you square to get 16?
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And it's four, right?
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But we also saw that negative four squared equals 16.
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Well, when you use a radical symbol and say what is the square root of 16, we give what
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we call the principal root, which is always positive.
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One thing to remember, whenever you take the square root of a number, the answer will
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always be positive.
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So keep that in mind.
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Okay, so the square root of 16 is four because four squared is 16, Charlie.
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All right.
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Let's look at some other square roots.
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Now before we move on though, let's look at what we call perfect squares.
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Now watch, Charlie, what's zero squared?
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Zero.
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Zero, that's right.
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So zero is considered a perfect square, which means when you're asked what is the square
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root of zero, the answer will be zero because zero squared is zero.
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It's so easy, it's confusing.
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Now like this one, Charlie, one is a perfect square because one squared is one.
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Therefore the square root of one will be one, right?
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Think about that one.
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Now here's this one.
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Four is also a perfect square because two squared is four.
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Therefore, Charlie, if somebody asks you what is the square root of four, what's the answer?
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Two.
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Two, that's right.
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And other perfect squares are nine because three squared is nine.
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We have 16 because four squared is 16.
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Twenty-five is a perfect square because five squared is 25.
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And 36 is a perfect square because six squared is 36.
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And of course, there's a whole lot more, right?
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We'll stop there for now.
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All right, Charlie, let's do some problems.
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What is the square root of 36, Charlie?
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Six.
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Six because six squared is 36.
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Remember, square roots, we always give positive answers.
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The principal root.
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Okay, Charlie, how about the square root of 49?
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Seven.
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Seven because seven squared is 49.
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Now, Charlie, what's the square root of 144?
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12.
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12 because 12 squared is 144, right?
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Okay, we're dealing with perfect squares here.
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Charlie, what's the square root of 64?
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Eight, eight because eight times eight is 64.
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What's the square root of 100?
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10.
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10 because 10 squared is 100.
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Now pay attention, this one, Charlie, don't get scared.
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What's the square root of 10?
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Uh-huh.
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That's right.
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10 is not a perfect square.
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Therefore, we have to use a calculator.
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Now, the square root of nine is three.
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So the square root of 10 should be a little bit more than three.
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And Charlie, if you take your calculator out and calculate the square root of 10, you
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will get a number 3.162, which is a little bit bigger than three, right?
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In this class, at this time, we're only going to deal with square roots of perfect squares.
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Okay?
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All right.
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Yeah, Charlie.
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We're going to look at what we call a right triangle.
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Okay?
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This is a word problem.
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Now a right triangle means it has a right angle.
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And the sideline opposite the right angle, which is that 13, Charlie, is called the hypotenuse.
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And the 5 and the A are referred to as the legs of the triangle.
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Now when you have a right triangle, we have a theorem, which is called the Pythagorean
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theorem.
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And it's only applied to right triangles like this.
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And that theorem is up there, c squared equals a squared plus b squared.
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Now we're going to use that theorem to solve for that sideline to A, right?
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Find that sideline to A.
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Okay?
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Now in the theorem, c represents the sideline opposite the right angle, which is called
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the hypotenuse, the longest side.
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The A and the B represent what we call the legs of the triangle.
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And here we have a label there, the hypotenuse, this 13, Charlie.
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The legs are five inches and A. And we're trying to find A.
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So here we go, Charlie.
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There's a theorem.
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So this is called the B squared equals A squared plus b squared.
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Our c is that 13.
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Our a is that leg right there and the other leg will call it five.
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Okay?
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Now, Charlie, what's 13 squared?
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169.
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That's a tough one there.
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And five squared is 25.
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Very nice.
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Now we're going to solve for A squared.
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And so what do we do?
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So track 25.
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That's right.
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And so we get 169 to track 25 is 144.
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That's right.
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And our right hand side we're left with a squared.
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So 144 equals A squared, Charlie.
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So Charlie, what number do you square to get 144?
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12.
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That's right.
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So 12 should equal A. Well, if 12 equals A, that means A equals 12.
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And so that's our missing sideland.
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And you can see, if you take 12 squared, which is 144 plus five squared, which is 25, you'll
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get 169.
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And if you take the square root of 169, you get 13.
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So the theorem does work.
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That's a tough problem there, right?
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Okay.
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We're going to do more of those later.
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Anyway, let's do some square root problems now.
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Here we go, Charlie.
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The square root of four plus square root of nine, we don't need catheters for this.
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What's the square root of four?
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Two.
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And the square root of nine?
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Three.
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And what's two plus three?
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Five.
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Very nice.
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Okay.
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Here's another one.
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16 subtract square root of 25.
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What's the square root of 16?
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Four.
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Square root of 25?
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Five.
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Very nice.
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What's four subtract five?
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Negative one.
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Negative one.
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No catheter required.
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Let's do another one.
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Try and don't get scared.
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Three square roots of 64 means three times the square root of 64.
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Two square roots of 49 means two times the square root of 49, Charlie.
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So we have three times what's the square root of 64?
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Eight.
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Eight.
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Plus, subtract two times the square root of 49, which is seven.
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Seven.
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There we go.
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And three times eight is 24.
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Two times seven.
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14.
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And 24 is a truck 14.
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10 is 10.
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Very nice, Charlie.
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All right.
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Let's do one more.
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Now, don't get scared.
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Notice we have fractions underneath the radical sign.
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So what fraction do we square to get 25 over nine, Charlie?
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Five thirds?
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That's right.
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A lot of people like to think, well, the square root of 25 is five, and the square root of
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nine is three.
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So that is five thirds, right?
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Because five thirds squared means five thirds times five thirds, which is 25 over nine,
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right?
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So the square root of 25 over nine is five thirds.
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What's the square root of anyone over 16, Charlie?
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Negative one.
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Very nice there, nine over four.
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And here we have to find the LCD, which is 12.
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Okay.
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Now we're going to use some kung fu.
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Remember, I'll work this one for you.
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Three goes into 12.
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Four times four times five is 20.
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Four goes into 12.
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Three times nine is 27.
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And remember, it's over 12, because these are 12s.
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And 20 plus 27 is 47, and it's over 12, that's our answer, 4712s.
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It was some good kung fu there.
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Now notice we did all these without a calculator, right?
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So anyway, you better be ready to do these without a calculator on the next exam.
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Anyway, that's it for now.
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We'll see you again soon.