Square Root of 332
2026-02-28 10:16 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-332

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 332, we need to group it as 32 and 3.

Step 2: Now we need to find n whose square is <= 3. We can say n is ‘1’ because 1 x 1 = 1, which is less than 3. Now the quotient is 1, and after subtracting 1 from 3, the remainder is 2.

Step 3: Now let us bring down 32, which is the new dividend. Add the old divisor with the same number: 1 + 1 = 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 ≤ 232. Let us consider n as 9, now 2 x 9 x 9 = 162.

Step 6: Subtract 162 from 232, the difference is 70, and the quotient is 19.

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 7000.

Step 8: Now we need to find the new divisor that is 389 because 389 x 9 = 3501.

Step 9: Subtracting 3501 from 7000 we get the result 3499.

Step 10: Now the quotient is 18.9.

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

So the square root of √332 ≈ 18.22