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1225 happens to be a perfect square and, if you happen to know that, from the context of the question, then trial and error is probably best. Since the last two digits are 25 the units digit must be 5. 30-squared is 900: too small and 40-squared is 1600: too large so the square root must be between 30 and 40. A 2-digit number, between 30 and 40, whose units digit is 5? Wonder what that can be? Yes, it is! 35!

A more systematic method for square roots, in general, consists of starting with an initial estimate, then dividing the number by the estimate. Then calculate the average between the initial estimate and the result, and use this for your next estimate. For example, you want to calculate the square root of 2, and use 1 as your initial estimate. 2 / 1 = 2, so you take the average of 1 and 2 for your next estimate. That would be 1.5. Next step: 2 / 1.5 = 1.33; average between 1.5 and 1.33 is 1.42. This is already fairly close to the square root of 2, but you can continue this process to get more significant digits.

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Wiki User

12y ago
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AnswerBot

1y ago

The square root of 1225 is 35.

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Q: How do you work out the square root of 1225?
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