Welcome to the amazing world of mental math! Today we'll learn incredible tricks to calculate squares of any number in your head. These techniques will make you faster than a calculator and impress everyone around you. Let's start this mathematical adventure!
Our first trick is for numbers ending in 5. This is incredibly simple! Take the digits before 5, multiply by the next consecutive number, then append 25. For example, 35 squared: take 3, multiply by 4 to get 12, append 25 to get 1225. Let's try 105 squared: take 10, multiply by 11 to get 110, append 25 to get 11025. Amazing, right?
The second trick uses algebraic identities. Break your number into a sum or difference where one part is easy to square. For 52 squared, write it as 50 plus 2 squared. Using the formula, we get 50 squared plus 2 times 50 times 2 plus 2 squared, which equals 2500 plus 200 plus 4, giving us 2704. For 48 squared, we use 50 minus 2 squared, getting 2500 minus 200 plus 4, which equals 2304.
The third trick uses difference of squares. For any number N, we can write N squared as N minus b times N plus b, plus b squared. Choose b to make one factor a round number. For 52 squared, choose b equals 2, giving us 50 times 54 plus 4, which equals 2700 plus 4, or 2704. For 97 squared, choose b equals 3, giving us 94 times 100 plus 9, which equals 9409.
Our final trick is the Vedic base method, perfect for numbers near powers of 10. Choose a base close to your number and find the deviation. For 103 squared with base 100, deviation is plus 3. Left part is 103 plus 3 equals 106, right part is 3 squared equals 09, giving us 10609. For 112 squared, deviation is plus 12. Left part is 112 plus 12 equals 124, right part is 144, but we need only 2 digits, so 44 with carry 1, making 125 and 44, or 12544. Congratulations! You now know four powerful mental math tricks!