Square Root of 9000
2026-02-28 11:17 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-9000

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, we need to group the numbers from right to left. In the case of 9000, we need to group it as 90 and 00.

Step 2: Now we need to find n whose square is less than or equal to 90. We can say n is '9' because 9 x 9 = 81, which is less than 90. Now the quotient is 9, and after subtracting 81 from 90, the remainder is 9.

Step 3: Now let us bring down 00, making the new dividend 900. Add the old divisor with the same number: 9 + 9 = 18, which will be our new divisor.

Step 4: The new divisor will be 18, and we need to find the value of n.

Step 5: The next step is finding 18n × n ≤ 900. Let us consider n as 5; now 18 x 5 = 90, and 90 x 5 = 450, which is less than 900.

Step 6: Subtract 450 from 900; the difference is 450, and the quotient is 95.

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 45000.

Step 8: Now we need to find the new divisor, which is 189 because 1895 x 5 = 9475, which is less than 45000.

Step 9: Subtracting 9475 from 45000 gives a result of 35525.

Step 10: The quotient is 94.8.

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

So the square root of √9000 is approximately 94.87.