Find Square Roots of Big Numbers in Seconds! (No Calculator Needed)

Before we drive in, can you figure out the square root of 4624 in just 5 seconds? Was that tough? I bet over 90% of the audience couldn't crack it right away. But don't worry, because today I'm going to teach you a mind-blowing trick to find the square root of any perfect square number mentally. No calculator, no pen and paper, and by the time you finish watching this video, you'll be solving square roots within seconds. Excited? Let's start. The only thing you need to remember is the squares of numbers from 0 to 9 like these. Easy, right? I'm sure you already know these. Now focus on the last digits of each square. I've highlighted them for you because this is the real magic. Notice that some of these squares end in the same last digit. 1 squared and 9 squared both ended 1. 2 squared and 8 squared both end in 4. 3 squared and 7 squared both end in 9. And 4 squared and 6 squared both end in 6. The square root of 0 ends in 0, and the square root of 5 ends in 5. That's different from all the other squares listed here. Let's begin with a simple one. What's the square root of 625? Focus on the last digit of this number, which is 5. From our magic sheet, now look at the square whose last digit ends up in 5. It's 5 by itself. So write down 5 here. Now cut off the last two digits. We're left with 6. Again from this sheet, find out what's the biggest square, which is less than or equal to 6. That's 2 squared is equal to 4, so write down 2 here. That's it. We are done. The final answer is 25. See how smoothly we are able to solve it. Now let's take another example. What's the square root of 841? Look at the last digit of this number. It's 1. From our sheet, which squares have last digits ending in 1? It could be 1 squared is equal to 1, or 9 squared is equal to 81. So write down 1 and 9 as our possible last digits. Now as we did before, cross out the last two digits. We're left with 8. Again from the sheet, what's the biggest square less than or equal to 8? That's 4, which is 2 squared. So write down 2. Therefore, our answer will be either 21 or 29. To find the correct one, take this 2 and multiply it by the next number. That is 3. So 2 times 3 is equal to 6. Now compare this 6 with the leftover number. 8. If it is less than 6, we select the smaller number, which will be 1. And if it is greater than 6, then we select the bigger number, or this 9. In this case, 8 is greater than 6. Hence, we select 9. Therefore, our final answer is 29. Amazing, isn't it? Now let us level up our gear and find the square root of 1296. Look at the last digit. 6. Check which digits squared end in 6. 4 squared is 16, and 6 squared is 36. So our answer can end in 4 or 6. Now ignore the last two digits. We're left with 12. Which square is closest to 12? 3 squared is 9. So we take 3. Therefore, the possible answers are 34 or 36. Take the 3 and multiply it by the next number. 3 times 4 is 12. Since 12 is equal to 12, we pick the bigger number. That is 6. So the square root of 1296 is 36. We just nailed it. Let's try a harder one. The square root of 8649. Here, the last digit is 9. From this chart, we know 3 squared is 9 and 7 squared is 49. Therefore, the last digit of the answer is 3 or 9. Now look at the first part. 86. Which square is just below 86? That's 9 squared, which is 81. Now multiply 9 by 10 to get 90. Compare it with 86. Since 86 is less than 90, we'll consider 3. There we go. The square root of 8649 is 93. Awesome. Alright, we're going full pro level now. We're going to crack the square root of 11664. First, check the last digit. It's a 4. From our magic square list, we know 2 squared is 4 and 8 squared is 64. That means our answer will end in either a 2 or an 8. Next, hide away the last two digits. Now we're looking at 116. Which perfect square is just below that? It's 100. That's 10 squared. Take that 10 and multiply it by the next number. 11. You get 110. Now compare. Is 116 greater than 110? Yes. So we choose the bigger last digit. 8. Put it all together. And boom. Our answer is 108. Superb. You just crushed it like a math ninja. Now that you've seen the trick in action, let's test you one last time. What's the square root of 4624? You should be able to answer this in less than 5 seconds now. If this video helps you learn a new mental math skill, please consider hitting the like button, sharing it with friends, and subscribe for more awesome tricks.