Square Root Procedures

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You can find the square root of a number by following a very specific procedure. Learn about square root procedures with help from a mathematics educator in this free video clip.

Part of the Video Series: Mathematics Equations & More
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Video Transcript

Hi, I'm Jimmy Chang and we're here to discuss square root procedures. Now square roots are one of those things that takes a little bit getting used to but at the end of the day it really depends on what kind of numbers you have within the square roots. So we'll do a couple of examples going forward. Now suppose you have a square root of nine. Now nine is what we call a perfect square. Numbers that have perfect squares are really easy to simplify so the more of those you have, the easier they are to take care of. Now being that nine is a perfect square because you know three times three is nine. That's why the square root of nine is three. Because what number multiplied by itself is going to give you nine? It's going to be the number three. Now if you have square root of 25, you have to ask yourself the same question. What number multiplied by itself gives you 25? That's going to be five. Now one of the things you want to keep in mind here though is you do not want to really have a square root of a negative number because no real number multiplied by itself is going to give you the number on the inside. So for example square root of negative 16. It is not real number. Now, suppose you have something a little bit more involved like square root of 45. You know that no number multiplied by itself is going to give you 45. But that's not to say that you can't break it up into pieces to where you might be able to simplify it a little bit. Now one pair of numbers that multiply to give you 45 that a lot of people think about is nine times five. Now when you have a number that's not a perfect square, you want to think about OK what two numbers will multiply to give you the number on the inside one of which will be a perfect square. So since nine times five is equal to 45, what you can think about is square root of nine times five. Notice I rewrote the 45 as nine times five. Now there are some square root rules out there that allows you to break it up into two separate terms, so this will be square root of nine times square root of five. Now we can't do anything with the five because square root of five is prime, but square root of nine is three, so think of this as three square root of five. Now you can do this for multiplication you can do this with division, it works the same way, but one thing you cannot do is with addition or subtraction. So for example if you have square root of 16 plus nine, you cannot break that up into two separate square roots like you did with multiplication and division. You have to add or subtract the number on the inside. So in this case, square root of 16 plus nine, you have to add the two numbers so you have square root of 25. But as you know, square root of 25 is equal to five. So I'm Jimmy Chang, and that's a brief overview of square root procedures.

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