Square Root of 734
2026-02-28 09:10 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-734

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 734, we need to group it as 34 and 7.

Step 2: Now we need to find n whose square is less than or equal to 7. We can say n is ‘2’ because 2 × 2 = 4, which is less than 7. Now the quotient is 2. After subtracting 4 from 7, the remainder is 3.

Step 3: Now bring down 34, making the new dividend 334. 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.

Step 5: The next step is finding 4n × n ≤ 334. Let us consider n as 7, now 4 × 7 × 7 = 329.

Step 6: Subtract 329 from 334, the difference is 5, and the quotient is 27.

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 zeros to the dividend. Now the new dividend is 500.

Step 8: Now we need to find the new divisor that is 541 because 541 × 1 = 541.

Step 9: Subtracting 541 from 500 is not possible, so consider 27.0 and continue the process until you have two decimal places.

The square root of √734 is approximately 27.086.