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Example:

a)      Basic approach

=, because 12,5 is the half of 25 and the root of 25 is 5.

b)      Review

2,5 · 2,5 12,5. For 2,5 ∙ 2,5 is equal to 6, 25.

c)      Testing

We know that three is too small because 3 ∙ 3 = 9 < 12,5. On the other hand, four is too big because 4 ∙ 4 = 16. So the requested number lies between 3 <  and < 4.

3,5 is too small: 3,5 ∙ 3,5 = 12, 25 < 12, 5. But 3,6 is too big again, since 3,6 ∙ 3,6 = 12,96 > 12,5. So for the requested number, the following applies: 3,5 <  < 3,6.

3,51² = 12,3201
3,52² = 12,3904
3,53² = 12,4609
3,54² = 12,5316
3,55² = 12,6025
3,56² = 12,6736
3,57² = 12,7449
3,58² = 12,8164
3,59² = 12,8881

The root of 12,5 is 3,54, but the method to figuring this out is a little complicated.

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02/09/07