The technique I’m about to teach you is only useful for smaller numbers. As numbers get bigger, this technique’s resourcefulness vanishes. Have you ever felt the urge to calculate the squares of numbers without actually multiplying the number in a piece of paper? Well, there is in fact a simple way to do this. However, to really accomplish at this technique, one MUST memorize some basic squares.
All of us must know the squares of 1-10 by heart, or if one’s really gifted, 1-20 (For the extra-ordinary ones out there who have memorized even more squares, I salute your endeavor!). Now, say you are asked to find the square of 21, but you need to do it really fast. How can you do it?
Firstly, you absolutely MUST remember the square of 20, which is easy, 400. I’m going to be putting all square numbers in bold. Remember, we needed to find the square of 21. Add the preceding number and the number itself (i.e 20+21) to the square of the preceding number (which we know is 400). This gives us 441, which is, in fact, the square of 21!
Continuing this process, we can find the squares of more and more numbers. Instead of trying to remember all those wacky squares of huge numbers, one can proceed in this manner, step-by,step. It’s a peach if you have time pressure, and it also helps you remember the squares of the numbers easily. Once you start practicing in this way, you’ll find yourself being able to re-call the squares of the numbers much sooner than you could have ever achieved in the past!
To test if this technique is correct, let us calculate the squares of the numbers from 11-20, starting with the knowledge that the square of 10 is 100.
Thus,
112= 100 +10 +11 = 121
122= 121 +11 +12 = 144
132= 144 +12 +13 = 169
142= 169 +13 +14 = 196
152= 196 +14 +15 = 225
162= 225 +15 +16 = 256
172= 256 +16 +17 = 289
182= 289 +17 +18 = 324
192= 324 +18 +19 = 361
202= 361 +19 +20 = 400
As you can see (or if you’re not sure, go and grab a calculator or some pen and paper!), the squares of the number are accurate. If you have any queries, feel free to comment!
All of us must know the squares of 1-10 by heart, or if one’s really gifted, 1-20 (For the extra-ordinary ones out there who have memorized even more squares, I salute your endeavor!). Now, say you are asked to find the square of 21, but you need to do it really fast. How can you do it?
Firstly, you absolutely MUST remember the square of 20, which is easy, 400. I’m going to be putting all square numbers in bold. Remember, we needed to find the square of 21. Add the preceding number and the number itself (i.e 20+21) to the square of the preceding number (which we know is 400). This gives us 441, which is, in fact, the square of 21!
Continuing this process, we can find the squares of more and more numbers. Instead of trying to remember all those wacky squares of huge numbers, one can proceed in this manner, step-by,step. It’s a peach if you have time pressure, and it also helps you remember the squares of the numbers easily. Once you start practicing in this way, you’ll find yourself being able to re-call the squares of the numbers much sooner than you could have ever achieved in the past!
To test if this technique is correct, let us calculate the squares of the numbers from 11-20, starting with the knowledge that the square of 10 is 100.
Thus,
112= 100 +10 +11 = 121
122= 121 +11 +12 = 144
132= 144 +12 +13 = 169
142= 169 +13 +14 = 196
152= 196 +14 +15 = 225
162= 225 +15 +16 = 256
172= 256 +16 +17 = 289
182= 289 +17 +18 = 324
192= 324 +18 +19 = 361
202= 361 +19 +20 = 400
As you can see (or if you’re not sure, go and grab a calculator or some pen and paper!), the squares of the number are accurate. If you have any queries, feel free to comment!
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