Square Root of 535
2026-02-28 17:33 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-535

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 535, we need to group it as 35 and 5.

Step 2: Now we need to find n whose square is ≤ 5. We can say n as ‘2’ because 2 × 2 is 4, which is lesser than or equal to 5. Now the quotient is 2, and after subtracting 4 from 5, the remainder is 1.

Step 3: Now let us 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 4n. We need to find the value of n such that 4n × n ≤ 135. Let us consider n as 3, now 43 × 3 = 129.

Step 5: Subtract 129 from 135; the difference is 6. The quotient is 23.

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 600.

Step 7: Now we need to find the new divisor that is 463, because 463 × 1 = 463.

Step 8: Subtracting 463 from 600, we get the result 137.

Step 9: Continue doing these steps until we get two numbers after the decimal point.

So the square root of √535 is approximately 23.15.