Shortcut Method for Squaring Two-Digit Numbers

The video tutorial explains a shortcut method for squaring any two-digit number. It begins by determining the distance from the number to the nearest multiple of ten, then adjusts the factors accordingly and adds the square of the distance. An example using the number 23 is provided, demonstrating the method's flexibility with different multiples of ten. The tutorial concludes with a mathematical proof showing the method's validity for any two-digit number.

What is the first step in the shortcut method for squaring a two-digit number?

• Subtract ten from the number

• Add the number to itself

• Determine the distance to the nearest multiple of ten

• Multiply the number by ten

In the example of squaring 23, what is the nearest multiple of ten used?

• 10

• 25

• 30

• 20

What is the result of 20 times 26 plus 3 squared in the example provided?

• 529

• 520

• 530

• 540

How many units is 23 from the multiple of ten used in the alternative approach?

• 10

• 7

• 5

• 3

What is the expression obtained when using the alternative approach with 23 squared?

• 20 times 26 plus 3 squared

• 30 times 16 plus 7 squared

• 25 times 18 plus 5 squared

• 15 times 28 plus 8 squared

In the proof, what does the expression 10X plus Y represent?

• A four-digit number

• A single-digit number

• A three-digit number

• A two-digit number

What is the result of multiplying 10X by 10X in the proof?

• 20X squared

• 100X squared

• 10X squared

• 50X squared

What is the purpose of the mathematical proof in the video?

• To explain the history of squaring numbers

• To demonstrate a new method for addition

• To prove the shortcut method is valid

• To show the shortcut method is invalid

What is the final expression on the left side of the equation in the proof?

• 100X squared plus 30XY plus Y squared

• 50X squared plus 20XY plus Y squared

• 100X squared plus 10XY plus Y squared

• 100X squared plus 20XY plus Y squared

What does the conclusion of the proof confirm about the shortcut method?

• It is only valid for numbers greater than 50

• It is not applicable to any numbers

• It is valid for evaluating the square of any two-digit number

• It is only valid for numbers less than 20