Math CentralQuandaries & Queries


Question from Sandra, a parent:

What whole number equals 25 when it is squared and 125 when it is cubed?

Hi Sandra,

25 is a small enough number that you can do this by trial and error. You want a number which when squared is 25.

  • 2 squared is $2 \times 2 = 4$ so that's too small.
  • 3 squared is $3 \times 3 = 9$ which is still too small.

What about 4, 5, 6, ...?

When you find a number which has 25 as its square, what is its cube?


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