Square Root of 263
2026-02-28 10:37 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-263

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 263, we need to group it as 63 and 2.

Step 2: Now we need to find n whose square is less than or equal to 2. We can say n as ‘1’ because 1 × 1 is less than or equal to 2. Now the quotient is 1, and after subtracting 1 from 2, the remainder is 1.

Step 3: Now let us bring down 63, making the new dividend 163. Add the old divisor with the same number 1 + 1, we get 2, which will be our new divisor.

Step 4: We need to find the new digit of the divisor such that 2n × n ≤ 163. Let us consider n as 6. Now 26 × 6 = 156.

Step 5: Subtract 156 from 163, the difference is 7, and the quotient is 16.

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 700.

Step 7: Now we need to find the new divisor, which is 162. Multiply 162 × 4 = 648.

Step 8: Subtracting 648 from 700 we get the result 52.

Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.

So the square root of √263 ≈ 16.217.