Square Root of 739
2026-02-28 12:53 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-739

The long division method is particularly useful 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, group the numbers from right to left. For 739, group it as 39 and 7.

Step 2: Now find n whose square is ≤ 7. We can say n is ‘2’ because 2 × 2 = 4, which is ≤ 7. The quotient is 2, and after subtracting 4 from 7, the remainder is 3.

Step 3: Bring down 39, making the new dividend 339. Add the old divisor with the same number, 2 + 2 = 4, to get a new divisor.

Step 4: Now find the largest n such that 4n × n ≤ 339. Let’s consider n as 8. Now, 48 × 8 = 384, which is greater than 339. Trying n as 7, we get 47 × 7 = 329, which is less than 339.

Step 5: Subtract 329 from 339, the difference is 10, and the quotient is 27.

Step 6: Since the dividend is less than the divisor, we add a decimal point and two zeroes to the dividend. The new dividend is 1000.

Step 7: Find the new divisor. The divisor is now 274, and we try n as 3, since 2743 × 3 = 8229. Continue these steps until we achieve the desired precision.

The square root of √739 is approximately 27.189.