Square Root of 252
2026-02-28 11:31 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-252

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 252, we need to group it as 52 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 x 1 is lesser than or equal to 2. Now the quotient is 1; after subtracting 1-1, the remainder is 1.

Step 3: Now let us bring down 52, which is the new dividend. Add the old divisor with the same number 1 + 1, we get 2, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 152; let us consider n as 7, now 27 x 7 = 189

Step 6: Subtract 152 from 189; since it doesn't fit, we adjust n to 6, making 26 x 6 = 156. Subtracting 156 from 152 gives a negative value, so we adjust again to 5, making 25 x 5 = 125 with remainder 27.

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 2700.

Step 8: Now we need to find the new divisor that is 315 because 315 x 8 = 2520.

Step 9: Subtracting 2520 from 2700, we get the result 180.

Step 10: Now the quotient is approximately 15.8.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Continue until the remainder is zero.

So the square root of √252 is approximately 15.874