If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:2:18

CCSS.Math:

which of the following real numbers are irrational well it'll just means it's not rational it means that you cannot express it as the ratio of two integers so let's see what we have here so we have the square root of 8 over 2 so square root of 8 if you take the square root of a number that is not a perfect square it is going to be irrational and then if you just take that an irrational number and you multiply it and you divide it by any other numbers you're still going to get an irrational number so square root of 8 is irrational you divide that by 2 it is still irrational so this is not rational or another way of saying it is irrational now you have PI 3.14159 just keeps going on and on and on forever without ever repeating so this is irrational probably the most famous of all of the irrational numbers 5.0 well I can write I can represent 5.0 as 5 over 1 so 5.0 is rational it is not irrational 0.325 well this is the same thing as 325 over 325 over a thousand so I can clearly represent it as a ratio of integers so this is rational just as I could represent 5.0 is 5 over 1 both of these are rational they are not irrational here I have seven point seven seven seven seven seven seven and just keeps going on and on and on forever and the way we denote that you could just say these dots that say that the sevens keep going or you could say seven point seven and this line shows that the seven part the second seven just keeps repeating on forever now if you have a repeating decimal in other videos well actually try it will actually convert them into fractions but a repeating decimal can be represented as a as a ratio of two integers just as 1/3 is equal to 0.33 3 on and on and on or I could say like this I could say 3 repeating we can also do the same thing for that I won't do it here but this is rational so it's not irrational 8 and 1/2 well that's the same thing 8 and 1/2 is the same thing as 17 halves so it's clearly rational so the only two irrational numbers are the first two right over here