Square Root of 1026
2026-02-28 01:07 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1026

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 1026, we need to group it as 26 and 10.

Step 2: Now we need to find n whose square is less than or equal to 10. We can say n as ‘3’ because 3 × 3 = 9 is less than 10. Now the quotient is 3, and after subtracting 9 from 10, the remainder is 1.

Step 3: Bring down 26, making it the new dividend. 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 6n. We need to find the value of n.

Step 5: Find 6n × n ≤ 126. Let's consider n as 2, now 62 × 2 = 124.

Step 6: Subtract 124 from 126; the difference is 2, and the quotient is 32.

Step 7: 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 200.

Step 8: Find the new divisor, which is 64, because 642 × 3 = 192.

Step 9: Subtracting 192 from 200, we get the result 8.

Step 10: Now the quotient is 32.0

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

So the square root of √1026 is approximately 32.03.