Squaring a number when it is the midpoint between two numbers that are easier to multiply

Often the easiest 2-digit numbers to square are those who lie at the midpoint between two numbers that are easier to multiply.

Example: If the number to be squared is 97, it should be easily recognized as the midpoint between 100 and 94.

First, multiply 94 x 100 = 9400.

Next, add to this the square of the distance from the midpoint to one of the easily multiplied numbers. In this case, the distance is 3 and the square of 3 is 9. 9400 + 9 =9409.

Another example: If the number squared is 62, it is the midpoint between 60 and 64.

First, multiply 60 x 64 = 3840.

Next, add to this the square of the distance from the midpoint to one of the easily multiplied numbers. In this case, the distance is 2 and the square of 2 is 4. 3840 + 4 = 3844.

For the last example, let’s square 29. It is the midpoint between 30 and 28.

First, multiply 30 x 28 = 840.

Next, add to this the square of the distance from the midpoint to one of the easily multiplied numbers. In this case, the distance is 1 and the square of 1 is 1. 840 + 1 = 841.

For practice problems, square random numbers using these simple steps. Check your answers by calculator at first to build confidence. You will be surprised at how easily and quickly the answers will come to you, with practice.

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