Square Root of 1962
2026-02-28 08:53 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1962

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 1962, we need to group it as 62 and 19.

Step 2: Now we need to find n whose square is 19. We can say n as ‘4’ because 4 x 4 = 16 is lesser than or equal to 19. Now the quotient is 4, and after subtracting 16 from 19, the remainder is 3.

Step 3: Now let us bring down 62, which is the new dividend. Add the old divisor with the same number, 4 + 4 = 8, which will be our new divisor.

Step 4: The new divisor will be 8n, and we need to find the value of n.

Step 5: The next step is finding 8n x n ≤ 362. Let us consider n as 4, now 8 x 4 = 32, and 32 x 4 = 128.

Step 6: Subtract 128 from 362, the difference is 234, and the quotient is 44.

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 23400.

Step 8: Now we need to find the new divisor. It will be 889 because 889 x 9 = 8001.

Step 9: Subtracting 8001 from 23400, we get the result 15499.

Step 10: Now the quotient is 44.2

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

So the square root of √1962 is approximately 44.28.