Square Root of 905
2026-02-28 11:18 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-905

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 905, we need to group it as 05 and 9.

Step 2: Now we need to find n whose square is less than or equal to 9. We can say n is ‘3’ because 3^2 = 9. Now the quotient is 3; after subtracting 9 - 9, the remainder is 0.

Step 3: Now let us bring down 05, which is the new dividend. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.

Step 4: The new divisor will be 6n. We need to find the value of n such that 6n × n ≤ 05. Let us consider n as 0. Now 6 × 0 × 0 = 0.

Step 5: Subtract 5 from 0, the difference is 5, and the quotient is 30.

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 500.

Step 7: Now we need to find the new divisor that is 60n. Let n = 8, because 608 × 8 = 486.

Step 8: Subtracting 486 from 500, we get the result 14.

Step 9: Continue doing these steps until we get two numbers after the decimal point. The quotient is approximately 30.08.

So the square root of √905 is approximately 30.08.