Final answer:
To find the square root using division method, we divide the given number into pairs and find the largest digit 'x' that satisfies a specific condition. Then, we repeat this process until we find the desired square root.
Step-by-step explanation:
To find the square root using division method, we divide the given number into pairs starting from the rightmost digit.
(i) For √12544, we divide it into pairs as 12 and 54.
Then, we find the largest digit 'x' such that (2x) * x is less than or equal to 12. In this case, it is 3.
So, the first digit is 3 and the remainder is 12 - (3 * 3) = 3. We bring down the next pair '54' and repeat the process.
The next digit is 2 and the remainder is 54 - (32 * 2) = 54 - 12 = 42. Finally, we get the square root of 12544 as 32.3.
(ii) For √97344, we divide it into pairs as 97 and 34.
The largest digit 'x' such that (9x) * x is less than or equal to 97 is 9. So, the first digit is 9 and the remainder is 97 - (9 * 9) = 97 - 81 = 16.
Bringing down the next pair '34', the next digit is 8 and the remainder is 16 - (98 * 8) = 16 - 784 = -768.
As we have a negative remainder, we should pair the next two digits with the remainder and continue the process.
So, we pair 24 with -768.
The digit 'x' such that (98x) * x is less than or equal to -768 is 0.
Hence, the next digit is 0 and the remainder is -768 - (980 * 0) = -768. Finally, we get the square root of 97344 as 98.08.
(iii) For √286225, we divide it into pairs as 286 and 225.
The largest digit 'x' such that (28x) * x is less than or equal to 286 is 5. So, the first digit is 5 and the remainder is 286 - (28 * 5) = 286 - 140 = 146.
Bringing down the next pair '225', the next digit is 1 and the remainder is 146 - (156 * 1) = -10.
As we have a negative remainder, we should pair the next two digits with the remainder and continue the process.
So, we pair 00 with -10. The digit 'x' such that (156x) * x is less than or equal to -10 is 0.
Hence, the next digit is 0 and the remainder is -10 - (1560 * 0) = -10. Finally, we get the square root of 286225 as 56.10.
(iv) For √36360, we divide it into pairs as 36 and 36.
The largest digit 'x' such that (3x) * x is less than or equal to 36 is 6. So, the first digit is 6 and the remainder is 36 - (3 * 6) = 36 - 18 = 18.
Bringing down the next pair '36', the next digit is 3 and the remainder is 18 - (66 * 3) = 18 - 594 = -576.
As we have a negative remainder, we should pair the next two digits with the remainder and continue the process.
So, we pair 00 with -576.
The digit 'x' such that (663x) * x is less than or equal to -576 is 0.
Hence, the next digit is 0 and the remainder is -576 - (6630 * 0) = -576.
Finally, we get the square root of 36360 as 60.30.