Square Root of 637
2026-02-28 21:38 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-637

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 637, we need to group it as 37 and 6.

Step 2: Now we need to find n whose square is less than or equal to 6. We can say n is ‘2’ because 2 × 2 = 4 is less than 6. Now the quotient is 2, and after subtracting 4 from 6, the remainder is 2.

Step 3: Now let us bring down 37, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.

Step 4: The new divisor will be 4n, and we need to find the value of n such that 4n × n ≤ 237. Let us consider n as 5, now 45 × 5 = 225.

Step 5: Subtract 225 from 237, and the difference is 12. The quotient is now 25.

Step 6: 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 1200.

Step 7: Now we need to find the new divisor which is 505 because 505 × 2 = 1010.

Step 8: Subtracting 1010 from 1200, we get the result 190.

Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose there is no decimal value; continue till the remainder is zero.

So the square root of √637 ≈ 25.24.