Example: what is √20 ?Children first learn to find the easy square roots that are whole numbers, but quickly the question arises as to what are the square roots of all these other numbers. You can start out by noting that (dealing here only with the positive roots) since √16 = 4 and √25 = 5, then √20 should be between 4 and 5 somewhere.Then is the time to make a guess, for example 4.5. Square that, and see if the result is over or under 20
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.GuessSquare of guessHigh/low2.45.76Too 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).