Square Root of 2376
2026-02-28 01:43 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2376

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 2376, we need to group it as 76 and 23.

Step 2: Now we need to find n whose square is closest to 23. We can say n is ‘4’ because 4 × 4 = 16 is lesser than or equal to 23. Now the quotient is 4, and after subtracting 16 from 23, the remainder is 7.

Step 3: Now let us bring down 76, which is the new dividend. Add the old divisor with the same number 4 + 4 to get 8, which will be our new divisor prefix.

Step 4: We need to find the next digit n such that 8n × n ≤ 776. Let us consider n as 9, now 89 × 9 = 801, which is too large. Try n = 8, and 88 × 8 = 704, which is suitable.

Step 5: Subtract 704 from 776, the difference is 72, and the quotient is 48.

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 7200.

Step 7: Now we need to find the new digit n for the divisor 964n × n ≤ 7200. Let's try n = 7, where 487 × 7 = 3409, which fits.

Step 8: Subtracting 3409 from 7200, we get 3791.

Step 9: Continue this process until the desired accuracy is achieved.

So the square root of √2376 is approximately 48.7487.