Square Root of 10201
2026-02-28 08:36 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-10201

The long division method is useful for both perfect and 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 10201, we need to group it as 01, 20, and 10.

Step 2: Now we need to find n whose square is less than or equal to 10. We can use n = 3 because 3 x 3 = 9, which is less than 10. The quotient is 3, and the remainder is 1.

Step 3: Bring down the next pair 20 to make it 120. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.

Step 4: The new divisor will be placed beside the dividend to make it 6n as the new divisor. We need to find the value of n.

Step 5: The next step is finding 6n x n ≤ 120; let us consider n as 2, so 62 x 2 = 124, which is too large. Try n = 1, so 61 x 1 = 61.

Step 6: Subtract 120 - 61, and the difference is 59, and the quotient is 31.

Step 7: Bring down the next pair 01 to make it 5901. Add the old divisor with the same number 61 + 1 to get 62, which will be our new divisor.

Step 8: The next step is finding 62n x n ≤ 5901; let us consider n as 9, so 629 x 9 = 5661.

Step 9: Subtract 5901 - 5661, and the difference is 240, and the quotient is 310.

Step 10: 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 24000.

Step 11: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √10201 is 101.