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Archimedes and Numerical Roots

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

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Weekly Problem 22 - 2012
What number could replace * so that */5 is between 3 and 4?

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More or Less?

Are these estimates of physical quantities accurate?

Big and Small Numbers in Physics

Stage: 4 Challenge Level: Challenge Level:1

Note that most of the ideas used here are typically covered at school before the age of 16, although possibly in mathematics, physics or chemistry.

In estimation questions don't be afraid to have a go with a guess at some numbers in the problem and then to refine your estimate after checking it makes some sort of sense.

Although there is no 'right' answer to an estimation, there are good or bad estimates and sensible or over detailed calculations.

Think how you might make your estimation a good one, and think how it makes sense to ignore certain complexities in particular calculations.