Square Root of 1292
2026-02-28 08:37 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1292

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 1292, we need to group it as 92 and 12.

Step 2: Now we need to find n whose square is less than or equal to 12. We can say n as ‘3’ because 3 x 3 = 9 is lesser than or equal to 12. Now the quotient is 3, and after subtracting 9 from 12, the remainder is 3.

Step 3: Now let us bring down 92, making it the new dividend. Add the old divisor with the same number, 3 + 3, we get 6, which will be our new divisor.

Step 4: The new divisor will be 6n. We need to find the value of n such that 6n x n is less than or equal to 392. Let us consider n as 6, now 66 x 6 = 396.

Step 5: Subtract 396 from 392, getting -4, and the quotient is 36. Since the remainder is negative, n must be adjusted.

Step 6: Re-evaluate n and check that 65 x 5 = 325, and 392 - 325 = 67.

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 6700.

Step 8: Now we need to find the new divisor. 71 x 9 = 6399.

Step 9: Subtracting 6399 from 6700, we get the result 301.

Step 10: Now the quotient is 35.9

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

So the square root of √1292 is approximately 35.93.