Square Root of 74
2026-02-28 12:56 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-74

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, we need to group the numbers from right to left. In the case of 74, we need to group it as 74.

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 x 2 = 4, which is less than 7. Now the quotient is 2, after subtracting 4 from 7, the remainder is 3.

Step 3: Bring down 4, making the new dividend 34. Double the divisor, 2, to get 4.

Step 4: The next step is finding 4n × n ≤ 34. Let us consider n as 8; now 48 x 8 = 384, which is more than 34, so we try n as 7, and 47 x 7 = 329, which works.

Step 5: Subtract 329 from 340, the difference is 11, and the quotient is 8.6

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 zeros to the remainder. Now the new dividend is 1100.

Step 7: Find the new divisor, which is 86, because 860 x 1 = 860

Continue these steps until you get the desired decimal places. So the square root of √74 ≈ 8.602