What is the fastest mental method to calculate square of any number
let’s say 32 x 32, is a bit more difficult. the first step is to figure out the distance (more accurately the absolute value) from the number you’re squaring to the nearest multiple of ten. In our example, the nearest multiple of 10 to 32 is 30, and the distance between 32 and 30 is 2. If you were instead squaring 77, the nearest multiple of 10 is 80, and the distance between 80 and 77 is 3. Now that we’ve figured out this distance, all that we have to do to find the answer to the problem is multiply the number we get when we subtract this distance from the original number by the number we get when we add this distance to the original number, and then add the square of the distance to the result.
In our example, the method says that 32 x 32 must be equal to 30 (that’s the original number minus the distance of 2) times 34 (that’s the original number plus the distance of 2) plus 4 (that’s the square of the distance of 2). In other words, 32 x 32 = (30 x 34) + 4.
Because as long as you use the fact that 30 = 3 x 10 to make the multiplication problem easy (as in 30 x 34 = 3 x 10 x 34 = 3 x 340 = 1,020), this is now an easy problem to solve! Practice at it a bit, and you’ll see that the beauty of this method is that it turns a single problem that’s hard to solve in your head into multiple easy problems.
let’s say 32 x 32, is a bit more difficult. the first step is to figure out the distance (more accurately the absolute value) from the number you’re squaring to the nearest multiple of ten. In our example, the nearest multiple of 10 to 32 is 30, and the distance between 32 and 30 is 2. If you were instead squaring 77, the nearest multiple of 10 is 80, and the distance between 80 and 77 is 3. Now that we’ve figured out this distance, all that we have to do to find the answer to the problem is multiply the number we get when we subtract this distance from the original number by the number we get when we add this distance to the original number, and then add the square of the distance to the result.
In our example, the method says that 32 x 32 must be equal to 30 (that’s the original number minus the distance of 2) times 34 (that’s the original number plus the distance of 2) plus 4 (that’s the square of the distance of 2). In other words, 32 x 32 = (30 x 34) + 4.
Because as long as you use the fact that 30 = 3 x 10 to make the multiplication problem easy (as in 30 x 34 = 3 x 10 x 34 = 3 x 340 = 1,020), this is now an easy problem to solve! Practice at it a bit, and you’ll see that the beauty of this method is that it turns a single problem that’s hard to solve in your head into multiple easy problems.
