Square Root of 14900
2026-02-28 10:59 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-14900

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 14900, we need to group it as (1)(49)(00).

Step 2: Now we need to find n whose square is 1 or less. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 1. Now the quotient is 1, and after subtracting 1 from 1, the remainder is 0.

Step 3: Now let us bring down 49, 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: The new divisor will be 20n. We need to find the largest digit n such that 20n x n is less than or equal to 49. Let us consider n as 2, now 20 x 2 x 2 = 40.

Step 5: Subtract 49 from 40; the difference is 9. We bring down the next group, which is 00, making the new dividend 900.

Step 6: Now, double the quotient obtained so far to get 24, and find the new tentative divisor 240 + n such that (240 + n) x n ≤ 900. We find n as 3 because 243 x 3 = 729.

Step 7: Subtract 900 from 729 to get a remainder of 171.

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 17100.

Step 9: Now we need to find the new divisor, which is 244n + n, because 2446 x 6 = 14676.

Step 10: Subtracting 14676 from 17100, we get the result 2424.

Step 11: Continue doing these steps until we get the desired level of precision after the decimal point.

So the square root of √14900 is approximately 122.0655.