Square Root of 435
2026-02-28 13:34 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-435

The long division method is particularly used for non-perfect square numbers. In this method, we 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, group the numbers from right to left. In the case of 435, we group it as 35 and 4.

Step 2: Find n whose square is close to 4. We can say n as ‘2’ because 2 x 2 is 4. Now the quotient is 2, and after subtracting, the remainder is 0.

Step 3: Bring down 35, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.

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

Step 5: Find 4n × n ≤ 35. Consider n as 8; now 4 x 8 x 8 = 32.

Step 6: Subtract 32 from 35; the difference is 3, and the quotient is 20.

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 300.

Step 8: Find the new divisor, which is 208 because 208 x 1 = 208.

Step 9: Subtract 208 from 300; we get 92.

Step 10: Now the quotient is 20.8.

Step 11: Continue these steps until we get two numbers after the decimal point. If there is no decimal value, continue until the remainder is zero.

So the square root of √435 ≈ 20.86.