How to Calculate Square Roots without a Calculator Mental Minute Math

hi i'm sean gannon and this is minute math and let's learn how to do square roots in your head without calculator now the method i'm showing you here it's an approximation right because lot of times square roots are going to just kind of go on forever but we're here we got good approximation on how to do square roots quickly in your head now i'm going to show my steps obviously out so you can see it but these steps are pretty simple and by the end of this video you should be able to do it in your head let's start with the square root of 19 as an example want to first look at well the perfect square that's below the number we're looking for and the perfect square below 19 is 16 right so we have 16 here and 16 perfect square right is 4 squared right good to know so 16 is that number we're looking at here want to take the number we start with and subtract 16 from it and that gives me three okay so now we have that number three three divided by the square root of 16 which is four put it right there and we're going to multiply that denominator or divide the whole thing really by two so that's the same thing as right three-fourths times one-half if you want to think of it like that so we have three-fourths right we got that four here from the square root of 16 and 3 4 so we have 19 minus 16 gives me 3. divide that by 2 or multiply by one half and that's 3 8. or the decimal is 0.375 if remember correctly yeah we then take that 0.375 and add it to the perfect square of 16 the 4. so we have 4.375 we add that up and that's an approximation of square root of 19. now the square root of 19 and still an approximation form let me use your calculator i've written down is it four point three five eight eight nine eight nine dot dot goes on forever that's pretty darn close approximation right here that we can quickly do those steps and our head now let's go try another one square root of 27 same process perfect square below that is going to be 25 right 5 squared is equal to 25 from the first one below it so take 27 and minus 25 to it and get 2. take 2 divided by that 5 right here okay right 5 square being 25 and let's multiply it by one half little easier to see or denominator just multiply it by 2 and we have 2 over 10 or that's 0.2 as decimal we add that to 5 and we have 5.2 right here and that's our approximation for the square root of 27. what does it come out when you use your calculator well square root of 27 is 5.19615 going on forever and that's pretty darn close right square root of 27 we got to be 5.2 approximately and we can easily do that in our head well hey hope you learned something here on how to do square roots in your head and maybe you can you know surprise your friends or nice little party trick if you learned something and you had fun don't forget to subscribe to this youtube channel and like this video this helps us make more of these more fun videos for you and for everyone else so as always thanks for watching