Math CentralQuandaries & Queries


Question from sofie, a parent:

find two consecutive numbers with a product of 9506

Hi Sofie,

I'm going to use what teachers sometimes call the "guess-and-check" method. I don't like this term but I don't have a better one. The method is to make an intelligent approximation (guess) to the answer and then modify (check) the approximation if necessary.

You have two consecutive integers with a product of 9506. These two integers are very close together, they are consecutive, so for my approximation I am going to ask, what if the two numbers were the same? Say they are both x then

x2 = 9506.

I used my calculator and found

x = √9506 = 97.50.

Thus the two numbers should be close to 97. What are they?


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