Square Root of 186
2026-02-28 17:41 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-186

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 186, we need to group it as 86 and 1.

Step 2: Now we need to find n whose square is close to or equal to 1. We can say n as ‘1’ because 1 x 1 is equal to 1. Now the quotient is 1, after subtracting 1 from 1 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: 1 + 1 we get 2, which will be our new divisor.

Step 4: Using the new divisor, find n such that 2n x n ≤ 86. Let us consider n as 4, now 24 x 4 = 96, which is too large. Try n as 3, now 23 x 3 = 69.

Step 5: Subtract 86 from 69, the difference is 17, and the quotient is 13.

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 1700.

Step 7: Now we need to find the new divisor that is 266 because 266 x 6 = 1596.

Step 8: Subtracting 1596 from 1700 we get the result 104.

Step 9: Now the quotient is 13.6

Step 10: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero. So the square root of √186 ≈ 13.64