Square Root of 1476
2026-02-28 08:31 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1476

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 1476, we need to group it as 76 and 14.

Step 2: Now we need to find n whose square is less than or equal to 14. We can say n is ‘3’ because 3 x 3 = 9, which is less than 14. Now the quotient is 3, and after subtracting 9 from 14, the remainder is 5.

Step 3: Now let us bring down 76, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.

Step 4: Using the new divisor 6, find the largest single-digit n such that 6n x n is less than or equal to 576. Let n = 9: 69 x 9 = 621, which is too large. Try n = 8: 68 x 8 = 544.

Step 5: Subtract 544 from 576, the difference is 32, and the quotient is 38.

Step 6: Adding a decimal point allows us to add two zeroes to the dividend. Now the new dividend is 3200.

Step 7: Find the new divisor by adding 8 to the previous divisor, giving 76. Determine n such that 760n x n is less than or equal to 3200. The appropriate n is 4, where 764 x 4 = 3056.

Step 8: Subtract 3056 from 3200, resulting in 144.

Step 9: The quotient is now 38.4. Continue this process until the desired decimal precision is reached.

So the square root of √1476 is approximately 38.42.