Problem of the Month - February 2024

When a number is multiplied by itself, the answer is a perfect square. 

For example, 25 is a perfect square because 5 x 5 is 25. 

In how many ways can the number 1764 be written as the product (multiply) of two perfect squares?

Solution

1764 can be written as a product of two perfect squares in three ways.  

  • 4 x 441
  • 9 x 196
  • 36 x 49

(It can also be written as a product of three perfect squares 4 x 9 x 49)

 

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