Square Root of 25000
2026-02-21 20:35 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-25000

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 25000, we group it as 250 and 00.

Step 2: Now we need to find n whose square is closest to the first group (250). We can say n as ‘15’ because 15 x 15 = 225, which is less than 250. Now the quotient is 15, and after subtracting, the remainder is 25.

Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 15 + 15, we get 30, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 30n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 30n × n ≤ 2500. Let us consider n as 8; now 30 x 8 x 8 = 2400.

Step 6: Subtract 2500 from 2400; the difference is 100, and the quotient is 158.

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 10000.

Step 8: Now we need to find the new divisor, which is 316, because 316 x 3 = 948.

Step 9: Subtracting 948 from 1000, we get the result 52.

Step 10: Now the quotient is 158.11.

Step 11: Continue doing these steps until we get two numbers after the decimal point. So the square root of √25000 is 158.11.