how can we find the value of root
Answers
We find the value of root by prime factorization or by long division method.
#lovelove!
Step-by-step explanation:
Finding square roots by guess & check method
To find a decimal approximation to, say √2, first make an initial guess, then square the guess, and depending how close you got, improve your guess. Since this method involves squaring the guess (multiplying the number times itself), it uses the actual definition of square root, and so can be very helpful in teaching the concept of square root.
Example: what is square root of 20?
You can start out by noting that since √16 = 4 and √25 = 5, then √20 must be between 4 and 5.
Then make a guess for √20; let's say for example that it is 4.5. Square that, see if the result is over or under 20, and improve your guess based on that. Repeat this process until you have the desired accuracy (amount of decimals). It's that simple and can be a nice experiment for students!
Example: Find √6 to 4 decimal places
Since 22 = 4 and 32 = 9, we know that √6 is between 2 and 3. Let's guess (or estimate) that it is 2.5. Squaring that we get 2.52 = 6.25. That's too high, so we reduce our estimate a little. Let's try 2.4 next. To find the square root of 6 to four decimal places we need to repeat this process until we have five decimals, and then we will round the result.
Estimate Square of estimate High/low
2.4 5.76 Too low
2.45 6.0025 Too high but real close
2.449 5.997601 Too low
2.4495 6.00005025 Too high so the square root of 6 must be between 2.449 and 2.4495.
2.4493 5.99907049 Too low
2.4494 5.99956036 Too low, so the square root of 6 must be between 2.4494 and 2.4495
2.44945 5.9998053025 Too low, so the square root of 6 must be between 2.44945 and 2.4495.