Square Root of 286
2026-02-28 13:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-286

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 286, we need to group it as 86 and 2.

Step 2: Now we need to find n whose square is less than or equal to 2. We can say n is ‘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 86, which is the new dividend. Add the old divisor with the same number 1 + 1 to 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, and we need to find the value of n.

Step 5: The next step is finding 2n x n ≤ 186. Let us consider n as 8, now 28 x 8 = 224.

Step 6: Subtract 224 from 186, the difference is 62, and the new dividend is now 6200 after adding decimal points and zeros.

Step 7: Now we need to find the new divisor, which is 169, because 169 x 9 = 1521.

Step 8: Subtracting 1521 from 6200, we get the remainder 4680.

Step 9: Continue this process until we achieve a precise decimal value for the square root.

So, the square root of √286 is approximately 16.91.