How Fast Can YOU solve this? – Calculate!

追加: 2026-05-13

[00:00:00]Hello my lovelies. It's Susanna and today I want to show you two different ways how to calculate this in your head.

[00:00:08]We have 99 squared + 1. The first way is to take the 99 and square it. So it is 99 * 99.

[00:00:22]Because we have to do our calculations in our head. I don't want to just multiply these two numbers. I'm not able to do this in my head but there is an easier way because here we have 99 of these 99s. We can first take 100 of these 99s which would be too much but this is way easier to calculate. But then we have to subtract one of these 99s because we only wanted to have 99 of them.

[00:00:59]So 100 * 99 just means I take my 99 and add two zeros and then I subtract 99.

[00:01:10]And I can do this in my head and get a result of 9,81.

[00:01:17]This is this green result here. And then don't forget to add the other one here.

[00:01:25]So that in total we get a result of 9,82.

[00:01:31]This was the first way, but I want to show you a second way. I'm curious which way you picked, so please let me know in the comments. There are probably more ways than just these two. But another way would be to also start with a 99 squared, but I mean we were not very happy with squaring a 99. So the question is, can I write the 99 in a different way with easier numbers and then square this result later? And then I also have to add my one here at the end. But I can write the 99 because it's so close to the 100 as 100 minus one.

[00:02:19]And these are easy numbers to square. We just have to be careful how we get rid of these parentheses. Now we have something minus something and all of this squared. This is a special product and there is a formula we have to have in our head of course then uh that we can use to calculate this. The formula looks like this. If you have a minus b in parentheses and square this then you get a squared - 2 * a * b + b 2. Let's apply this formula here.

[00:03:07]We take a and square it. So 100 squared first. Then we have minus 2 * a * b. So 2 * the 100 times the 1. And then we have + b^ 2. So we square the one. And don't forget that you have the plus one here still at the end. Okay. 100^ 2AR is just the 10 and two more zeros minus 2 * 100 * 1 is 200 plus 1 squared is just one plus the other one so + 2 in total and these numbers here if we calculate this we get 9,82 so of course the same result but a different way. Let me know in the comments which way you prefer. I wish you a wonderful day and I hope to see you in one of my next videos.