SQUARING NUMBERS ENDING IN 5

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What is 15²? How about 25²? How would you find the answer? Can you tell the answer in 3 to 5 seconds?




Yes, there is a fast way of squaring numbers ending in 5. The method lies on the pattern being formed by the numbers upon squaring as related to the numbers being squared. Let's observe the pattern of the numbers.






    5² = 25

    15² = 225

    25² = 625

    35² = 1,225


We know already that 5² is equal to 25, that is 5² = (5)(5) = 25. Since the remaining numbers end in 5, expectedly the results should also end in 25.

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   15 ² = 225
   25 ² = 625 
   35 ² = 1225 


Now, let us look for the relationship between the remaining digits (aside from 5 and 25). The numbers are 
 
   1 and 2    where     2 = (1)(2)    
   2 and 6                  6 = (2)(3)    
   3 and 12              12 = (3)(4)
 
In the first pair of numbers, 2 is the product of 1 and the next consecutive number which is 2. Same as with the second pair, 6 is the result when 2 is multiplied to the number next to it which is 3. In the third pair, 12 is the product of 3 and 4.



Hence, when you square a number ending in 5, you simply multiply the remaining digit of the number, aside from 5, to the number next to it. Let us try to use it in the following numbers.

1. What is 45²?
   

        solution:

Since the other digit aside from 5 is 4, multiply it to the number next to it which is 5. That is

            (4)(5)= 20

Affix 25 to the result. The result is 2025.

Hence, 45² =. 2,025

1. Find the exact value of 55²?
   
   
   solution: 

                The number is 5. Multiply that to the next number 6.

                           (5)(6) = 30

                Affix 25 to it. That is 3,025.

                Hence, 55² = 3025.


Now, it's your turn. Try to find the value of the following in 5 seconds.

1. 65²
   
2. 75²
   
3. 85²
   
4. 95²
   
5. 105²

Posted in: Math Appreciation,Math Patterns