Square Root of 1492
2026-02-28 23:31 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1492

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 1492, we need to group it as 92 and 14.

Step 2: Now we need to find n whose square is less than or equal to 14. We can say n as ‘3’ because 3 x 3 = 9, which is less than 14. Now the quotient is 3, and after subtracting 9 from 14, the remainder is 5.

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

Step 4: The new divisor will be 6n. We need to find the value of n.

Step 5: The next step is finding 6n x n ≤ 592. Let us consider n as 9; now 69 x 9 = 621.

Step 6: Subtract 621 from 592; the difference is -29, indicating n was too large, so we try n = 8. Now 68 x 8 = 544.

Step 7: Subtraction gives a remainder of 48, and the quotient is 38.

Step 8: 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 4800.

Step 9: Continue the long division steps to get an approximate square root value accurate to two decimal places.

So the square root of √1492 ≈ 38.63