How To Calculate Cube Roots In Your Head

How To Calculate Cube Roots In Your Head


Hi, this is Presh Talwalkar. In this video I’m going to teach you how you can calculate cube roots (∛) in your head. Why would you ever want to do this? The Education Secretary Nicky Morgan was recently on TV and put on the hot seat. She was asked by a ten-year-old the question, “What Is the cube root of 125?” She refused to answer any math questions on TV and I understand that. But if she knew the trick in this video, she could have answered it very quickly and done many more math problems. So to do the trick, you first have to memorize the cubes of each number from 1 to 10. The cube of a number is the number multiplied by itself three times. So the cube of 1 is still 1. The cube of 2 is 8. The cube of 3 is 27. And I’m going to keep writing the cubes of each number. So you may know some of these. Otherwise, to do this trick you’ll have to memorize these ten numbers. Now once we’ve written down these cubes, I want you to focus on the very last digit of the number of the cube. So what’s important is that each of these 10 numbers end in a different last digit. And that’ll be very important to doing this trick. So this will be another thing you have to memorize. When you memorize these 10 digits, you should also remember the last digit. So an easy way to remember this is that for the numbers 1, 4, 5, 6, 9, and 0, the last digit is the same as the numbers. And for the numbers 2 and 8, and 3 and 7, the last digit flips. So the last digit for 2 is 8, and the last digit for 3 is 7 and vice versa. So let’s do the trick. What’s the cube root of 39,304? The first thing I want you to do is look at the last digit. The last digit of 39,304 is 4, which we’re going to put in a box. So we look up 4 in the last digit, and that corresponds to the number 4. So we write down the number 4. The next step is we ignore the last three digits of our number. So in 39,304, we’re going to just ignore the 304. And now we want to find the closest cube without going over. So 39 is between 27 and 64, so it’s actually closest to 27 without going over, which means it’s closest to the cube of 3. And that gives us the other part of our answer, which is 3. So here we have it, we put the numbers together and 34 Is the cube root of 39,304. So why would this ever be useful? So here’s a trick you can do. Ask someone to pick a number from 1 to 100, and just think about it secretly, don’t have them tell you the number. Have them cube the number on a calculator. And once they cube the number, they tell you the cube and you instantly can tell them the cube root by using this table and using the trick. So let’s imagine they tell you the number is 636,056. So we look at the last digit, which is 6, and when the last digit is 6, that corresponds to the number 6. And then we look at the, we ignore the last three digits and we look at 636. That’s between the cubes of 8 and 9, so we put 8. And therefore, the cube root is 86. So once you get used, once you’ve memorized this table, you’ll actually be able to do this very quickly. Let’s do another example. 185,193 We look at the last digit of 3. That corresponds to the number 7 because 3 and 7 flip. Then we ignore the last three digits and we look at 185. And that’s closest to the cube of 5 without going over. So that gives us the answer of 57. So it’s a pretty neat trick. And if you want to know how this works, you can click through. I’ve made a short video which gives a math proof. If you like this video, please subscribe to my channel. You can support me on Patreon to get exclusive rewards. Catch me on my blog MindYourDecisions, on Twitter @preshtalwalkar. And you can get my books listed on my website.

100 thoughts on “How To Calculate Cube Roots In Your Head

  1. Can i download your book for free because I am poor.l hope you will give me to download for free.Can you tell me please.

  2. I think your last example was wrong because 185 is closest to 6=216-185= 31 & 5=125+60=185
    I hope you understand

  3. Okay but for the last one 185 is closer 216 then 125 so wouldn't it be 6? 185 is 60 away from 125 but only 31 away from 216

  4. The closet to 185 is 216 , it’s not 125 so that means the number was supposed to be 6 and the result will become 67 it’s wrong man

  5. That doesn't work….trs this with 88*88*88(and this is literaly the second number i tried this with..(99 was the first one)

  6. How to identify a number which is not a cube of some degit. Like 59304. According to this process the answer will be 34 which will be wrong

  7. You said closest cube without going over .What’s the thing you are trying to do ? In case of last one 185193 – I understand you take 7 first then why you take 5 why didn’t you take 4 ?need clarification

  8. I actually multiplied the number by itself and then multipled it again. For example 6. 6×6=36, 36×6= 216. Just how I do it cuz it worked well on my sats

  9. It doesn't work for the cube root of 117649 which is 49 but according to this method it come up with ans 59🤨?
    So,can u please tell me reason behind this?

  10. How does it work for 48?
    The cube is 110,592 from last digit I get 8 den ignoring the last 3 digits the closest cube to 110 is 125 which is cube of 5..so the answer comes to be 58.

  11. You think you need education to be the secretary of education in America? You just need money and connections

  12. not working this trick try example : cube root of 18604
    By using your trick it will be 24 but it is not the right answer

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