Square Root of 1445
2026-02-28 11:41 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1445

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 1445, we need to group it as 45 and 14.

Step 2: Now we need to find n whose square is less than or equal to 14. We can say n is ‘3’ because 3 x 3 = 9 is less than or equal to 14. Now the quotient is 3; after subtracting 9 from 14, the remainder is 5.

Step 3: Now let us bring down 45, which is 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 the sum of the dividend and quotient. Now we have 6n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 545. Let us consider n as 9, now 69 x 9 = 621.

Step 6: Subtract 545 from 621; the difference is negative, so we need to try n as 8. So, 68 x 8 = 544.

Step 7: Subtracting 544 from 545, the difference is 1, and the quotient is 38.

Step 8: Since the remainder is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 100.

Step 9: The new divisor is 760 because 760 x 1 = 760.

Step 10: Subtracting 760 from 1000, we get a result of 240.

Step 11: Continue these steps until we get two decimal places.

So the square root of √1445 ≈ 37.998