Square Root of 282
2026-02-28 23:23 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-282

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 282, we need to group it as 82 and 2.

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

Step 3: Now let us bring down 82, 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 x n ≤ 182. Let us consider n as 8, now 28 x 8 = 224.

Step 6: Subtract 224 from 182, the difference is negative, so n must be less than 8. Try n = 7, now 27 x 7 = 189 which is still larger than 182.

Step 7: Try n = 6, now 26 x 6 = 156 which is less than 182.

Step 8: Subtract 156 from 182, the difference is 26, and the quotient is 16.

Step 9: 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 2600.

Step 10: Now we need to find the new divisor. Add the previous quotient, 16, to the divisor, 26, forming 272. Consider n as 9, 2729 x 9 = 24561, which is larger than 26000.

Step 11: Try n = 8, now 2728 x 8 = 21824, which is less than 26000.

Step 12: Subtract 21824 from 26000, the remainder is 4176, and the new quotient is 16.8.

Step 13: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value continue till the remainder is zero.

So the square root of √282 is approximately 16.79.