Square Root of 213
2026-02-28 23:19 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-213

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 213, we group it as 13 and 2.

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

Step 3: Bring down 13, which is the new dividend. Add the old divisor with the same number: 1 + 1 = 2, which will be our new divisor.

Step 4: The new divisor will be 2n. We need to find the value of n.

Step 5: Find 2n × n ≤ 113. Let us consider n as 4, now 24 x 4 = 96.

Step 6: Subtract 96 from 113; the difference is 17, and the quotient is 14.

Step 7: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1700.

Step 8: Find the new divisor, let’s say it is 145, because 145 x 5 = 725.

Step 9: Subtracting 725 from 1700 gives the result 975.

Step 10: Now the quotient is 14.5

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

So the square root of √213 is approximately 14.59.