Square Root of 2197
2026-02-28 01:11 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2197

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 2197, we need to group it as 97 and 21.

Step 2: Now we need to find n whose square is less than or equal to 21. We can say n is ‘4’ because 4 x 4 = 16, which is less than or equal to 21. Now the quotient is 4, and after subtracting 16 from 21, the remainder is 5.

Step 3: Now let us bring down 97, which is the new dividend. Add the old divisor with the same number 4 + 4, and we get 8, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 8n x n ≤ 597. Let us consider n as 7, which gives us 87 x 7 = 609, which is too large. So, n must be 6, giving us 86 x 6 = 516.

Step 6: Subtract 516 from 597, and the difference is 81, with the quotient as 46.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 8100.

Step 8: Now we need to find the new divisor, which is 933 because 933 x 9 = 8397.

Step 9: Subtracting 8397 from 8100 gives us a new remainder.

Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So, the square root of √2197 is approximately 46.87.