Square Root of 1525
2026-02-28 10:38 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1525

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 1525, we need to group it as 15 and 25.

Step 2: Now we need to find n whose square is 15. We can say n as ‘3’ because 3 x 3 = 9 is less than 15. Now the quotient is 3 after subtracting 9 from 15, the remainder is 6.

Step 3: Now let us bring down 25, making the new dividend 625. Add the old divisor with the same number: 3 + 3, we get 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 625. Let us consider n as 10, now 60 x 10 = 600.

Step 6: Subtract 600 from 625, the difference is 25, and the quotient is 30.

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 2500.

Step 8: Now we need to find the new divisor, which is 390 because 390 x 6 = 2340.

Step 9: Subtracting 2340 from 2500, we get the result 160.

Step 10: Now the quotient is 39.0.

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

So the square root of √1525 is approximately 39.05.