Square Root of 284
2026-02-28 18:00 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-284

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 284, we need to group it as 84 and 2.

Step 2: Now we need to find n whose square is 2. We can say n as ‘1’ because 1 × 1 is lesser than or equal to 2. Now the quotient is 1, after subtracting 1-2 the remainder is 1.

Step 3: Now let us bring down 84 which is the new dividend. Add the old divisor with the same number 1 + 1 we get 2 which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 184. Let us consider n as 6, now 26 × 6 = 156.

Step 6: Subtract 184 from 156, the difference is 28, and the quotient is 16.

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 zeroes to the dividend. Now the new dividend is 2800.

Step 8: Now we need to find the new divisor that is 8 because 328 × 8 = 2624.

Step 9: Subtracting 2624 from 2800 we get the result 176.

Step 10: Now the quotient is 16.8.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √284 is approximately 16.85.