Square Root of 486
2026-02-28 01:24 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-486

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 486, we group it as 86 and 4.

Step 2: Now we need to find n whose square is less than or equal to 4. We can say n is ‘2’ because 2 x 2 = 4. Now the quotient is 2, and after subtracting 4 - 4, the remainder is 0.

Step 3: Now let us bring down 86, which is the new dividend. Add the old divisor with the same number, 2 + 2, to get 4, which will be our new divisor.

Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 86. Let us consider n as 2, now 42 x 2 = 84.

Step 5: Subtract 86 from 84; the difference is 2, and the quotient is 22.

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 200.

Step 7: Now we need to find the new divisor that is 441 because 441 x 4 = 1764.

Step 8: Subtracting 1764 from 2000, we get the result 236.

Step 9: Now the quotient is 22.4.

Step 10: 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 √486 is approximately 22.04.