Square Root of 273
2026-02-28 08:51 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-273

The long division method is particularly used for non-perfect square numbers. In this method, we find the closest perfect square number for the given number. Let us learn how to find the square root using the long division method, step by step:

Step 1: To begin with, group the numbers from right to left. In the case of 273, we group it as 73 and 2.

Step 2: Now, find a number n whose square is less than or equal to 2. We can say n is ‘1’ because 1 x 1 is less than or equal to 2. The quotient is 1, and after subtracting 1 from 2, the remainder is 1.

Step 3: Bring down 73, making the new dividend 173. Add the previous divisor with the same number: 1 + 1 = 2, which will be our new divisor.

Step 4: The new divisor is now 2n. We need to find the value of n such that 2n x n ≤ 173. Let us consider n as 6, now 26 x 6 = 156.

Step 5: Subtract 156 from 173; the difference is 17, and the quotient is 16.

Step 6: Since the dividend is less than the divisor, we add a decimal point and two zeroes to the remainder. The new dividend is 1700.

Step 7: Find a new divisor. The new divisor is 326, and we find n as 5 because 326 x 5 = 1630.

Step 8: Subtract 1630 from 1700, we get the result 70.

Step 9: The quotient is now 16.5.

Step 10: Continue doing these steps until you get two decimal places. If there are no decimal values, continue until the remainder is zero.

So, the square root of √273 ≈ 16.52.