Square Root of 2007
2026-02-28 13:36 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-2007

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 2007, we need to group it as 07 and 20.

Step 2: Now we need to find n whose square is less than or equal to 20. We can say n is 4 because 4^2 = 16 is less than 20. The quotient is 4 after subtracting 20 - 16, the remainder is 4.

Step 3: Now let us bring down 07, making the new dividend 407. Add the old divisor with the same number 4 + 4, we get 8, which will be our new divisor.

Step 4: The next step is finding 8n × n ≤ 407. Let us consider n as 5, now 85 × 5 = 425, which is more than 407. Try n as 4, 84 × 4 = 336, which fits.

Step 5: Subtract 407 from 336, the difference is 71.

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 zeros to the dividend. Now the new dividend is 7100.

Step 7: Now we need to find the new divisor. Try 889 × 9 = 8001, too high. Try 888 × 8 = 7104, too high. Try 887 × 8 = 7096, which fits.

Step 8: Subtract 7100 from 7096, we get the result 4.

Step 9: Now the quotient is 44.8

Step 10: Continue doing these steps until we get two numbers after the decimal point.

So the square root of √2007 is approximately 44.82.