Square Root of 6121
2026-02-28 10:11 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-6121

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 6121, we need to group it as 61 and 21.

Step 2: Now we need to find n whose square is close to 61. We can say n is ‘7’ because 7 × 7 = 49 is lesser than 61. Now the quotient is 7, and after subtracting 49 from 61, the remainder is 12.

Step 3: Now let us bring down 21, which is the new dividend. Add the old divisor with the same number, 7 + 7, to get 14, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 14n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 14n × n ≤ 1221. Let us consider n as 8; now 148 × 8 = 1184.

Step 6: Subtract 1184 from 1221, the difference is 37, and the quotient is 78.

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 3700.

Step 8: Now we need to find the new divisor that is 785 because 785 × 5 = 3925.

Step 9: Subtracting 3925 from 3700 gives a negative result, so we try with n = 4, and 784 × 4 = 3136.

Step 10: Subtracting 3136 from 3700, we get the result 564.

Step 11: The quotient is 78.2. Step 12: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero.

So the square root of √6121 is approximately 78.23.