Final answer:
The square root of 10816 is 104, which is obtained using the long division method by pairing digits, finding the largest square number less than each pair, and iterating the process until the square root is determined.
Step-by-step explanation:
To find the square root of 10816 using the long division method, we begin by pairing digits from right to left in groups of two, since we are dealing with a square root. For 10816, this gives us '10' and '81' and '16' as our pairs.
First, we find the largest square number less than or equal to 10, which is 1 (1×1=1). We subtract this from 10 and bring down the next pair of digits, '81', forming '981'.
Now, we look for a number that fits in the pattern (2x × x) <= 981, where 2x is the current result from the previous step appended to our new x on the right-hand side as the next digit, and x is the new digit we are trying to find. We find that 104 is the next number (104×4=416).
After subtracting 416 from 981 and bringing down the next pair '16', we have '5656'. We then find the next digit 'x' such that (208x × x) <= 5656. This turns out to be 1048 (1048×8=8384), which is too large, so we use 1044 (1044×4=4176).
Having subtracted 4176 from 5656, we get our remainder '1480', which when compared to the divisor (208x×x), indicates that there are no more digits to find, and the square root of 10816 is 104.
Therefore, we have found that:
- a. root of 10816 = 104
- b. root of 10816 = 104
- c. root of 10816 = 104
- d. root of 10816 = 104