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## Answers

Example: Find √6 to 4 decimal placesSince 22 = 4 and 32 = 9, we know that √6 is between 2 and 3. Let's just make a guess of it being 2.5. Squaring that we get 2.52 = 6.25. That's too high, so make the guess a little less. Let's try 2.4 next. To find approximation to four decimal places we need to do this till we have five decimal places, and then round the result.

__Guess__

__Square of guess__

__High/low__2.45.76Too low2.456.0025Too high but real close2.4495.997601Too low2.44956.00005025Too high, so between 2.449 and 2.44952.44935.99907049Too low2.44945.99956036Too low, so between 2.4494 and 2.44952.449455.9998053025Too low, so between 2.44945 and 2.4495.This is enough since we now know it would be rounded to 2.4495 (and not to 2.4494).