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Irrational Numbers

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alright today's math is everywhere topic of the day for unit 3 is rational versus irrational numbers today we're going to talk about what the difference is between an irrational number and an irrational number and how you can tell whether a certain number might be rational or irrational how are there irrational numbers what are irrational numbers and how are they different from rational those are all the kinds of things are in talk about today so let's start with a little review rational numbers irrational number is any number that can be written as a fraction or a ratio some examples 2/3 negative 1 111th 7 because it can be written as 7/1 negative 17 and .25 because 0.25 can be written as a fraction all right √ 64 is that a rational number or an irrational number well the square root of 64 is 8 and 8 as a rational number because you can write it is 8/1 what about the √ 4 that's irrational as well cuz it's two all whole numbers are rational cuz you can always write them is 2/1 or 8/1 what about a number like 81 if you take the square is 81 rational or irrational rational again this leaves the question what is irrational is anything irrational well here's another example if you have the square root of 36 that would come out to 6 because 6 x 6 x 36 6 is a perfectly rational number so the √ 36 comes out rational but if you had the √ 37 instead of √ 36 nothing times itself makes 37 37 isn't a nice square of a number so the only way you can find the square root of 37 is to use the square root button on a calculator if you do that you get some kind of crazy long decimal it probably takes up the whole screen of your calculator and it's a bunch of numbers that just kind of go on and on and on and this isn't like one of those nice cheating decimals like 3 3 3 3 3 3 3 3 3 or even one that has a pattern like 1-7 1-7 1-7 1-7 1-7 this is just a string of digits that has no pattern and that right there is what we call an irrational number and an irrational number happens when you try to take the square root of something that isn't a square of something and you can tell what are rational numbers bike because irrational numbers have decimals that keep on going forever and ever and ever but they ripped they go on forever without a repeating pattern there's no set pattern of numbers that keeps on going okay an irrational number is any number that cannot be written as a fraction because that crazy decimal stuff some examples are the square root of 2 or the square root of 3 or the square root of 5 are the √ 17 those are all irrational numbers because 2 isn't the square of anything and 3 isn't the square of anything and 5 and 17 aren't squares of anything so you can't square root them nice so those numbers turnout irrational okay so here's just a little bit more of an example √ 121 is 11 because 11 * 11 is 121 that's a nice rational number but the square root of 2 well if you punch it in your calculator you get something like that that's irrational there's no pattern to it okay and again your rational numbers keep on going without a pattern so let's check √ 4 is 2 is that rational or irrational that's rational √ 4 nights or the √ 4 is 2 + √ 9 is 3 so that could be like to do over 3 that's perfectly rational it's a ratio it's a fraction it's a rational number but the √ 7 yuck that just comes out to some weird decimal we don't know what it is but we definitely know that it is an ear rational number and there is your lesson rational numbers can be written as ratios irrational numbers can't because they're crazy crazy decimals that go on and on and on forever without any pattern and they're kind of yucky so here's your practice problems for this lesson number one makeup and example of a rational number any example you make one up practice problem to make up an example of an irrational number and an irrational number that you can think of to so that you understand what an irrational number is go ahead now go ahead and make up an example all right once you have that done you're done thanks a lot

Uploaded by Jeff Marbut.

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