Square Root of 4264
2026-02-28 23:53 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-4264

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 4264, we need to group it as 42 and 64.

Step 2: Now we need to find n whose square is closest to 42. We can say n is '6' because 6 x 6 = 36, which is less than or equal to 42. Now the quotient is 6 after subtracting 36 from 42, the remainder is 6.

Step 3: Now let us bring down 64, making the new dividend 664. Add the old divisor with the same number: 6 + 6 = 12, which will be our new divisor.

Step 4: We need to find a number n such that 12n x n ≤ 664. Let us consider n as 5, now 125 x 5 = 625.

Step 5: Subtracting 625 from 664, the difference is 39, and the quotient is 65.

Step 6: 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 3900.

Step 7: Find the new divisor. It will be 130.5 because 1305 x 3 = 3915, which is slightly more than 3900.

Step 8: Subtracting 3915 from 3900 gives a negative value, so adjust n to 2, making 1302 x 2 = 2604.

Step 9: Subtracting 2604 from 3900, we get a remainder of 1296.

Step 10: Continue this process until you get a satisfactory level of precision.

The square root of √4264 is approximately 65.287.